Given: WS bisects

Goal is to take at least 10,000 steps per day. According to your pedometer you have walked 5,274 steps. Write and solve an inequality to find the possible numbers of steps you can take to reach your goal. [U] Subtract off the existing steps (s) from your goal of 10,000[/U] g >= 10000 - 5274 [B]g >= 4726[/B] [I]Note: we use >= since 10,000 steps meets the goal as well as anytihng above it[/I]

Free Golden Ratio Calculator - Solves for 2 out of the 3 variables for a segment broken in 2 pieces that satisfies the Golden Ratio (Golden Mean).(a) Large Segment(b) Small Segment(a + b) Total Segment

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Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. How many minutes will it take until they're at the same altitude? Set up the Altitude function A(m) where m is the number of minutes that went by since now. Set up Graham's altitude function A(m): A(m) = 14040 - 50m <-- we subtract for descending Set up Max's altitude function A(m): A(m) = 12500 + 20m <-- we add for ascending Set the altitudes equal to each other to solve for m: 14040 - 50m = 12500 + 20m [URL=' type this equation into our search engine to solve for m[/URL] and we get: m = [B]22[/B]

Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older than her daughter, but 31 years younger than her mother (the grandmother). How old are the three Let grandmother's age be g. Let mother's age be m. Let daughter's age be d. We're given 3 equations: [LIST=1] [*]m = d + 25 [*]m = g - 31 [*]d + g + m = 150 [/LIST] This means the daughter is: d = 25 + 31 = 56 years younger than her grandmother. So we have: 4. d = g - 56 Plugging in equation (2) and equation(4) into equation (3) we get: g - 56 + g + g - 31 Combine like terms: 3g - 87 = 150 [URL=' this equation into the search engine[/URL], we get: [B]g = 79[/B] Plug this into equation (2): m = 79 - 31 [B]m = 48[/B] Plug this into equation (4): d = 79 - 56 [B]d = 23[/B]

Free Greatest Common Factor and Least Common Multiple Calculator - Given 2 or 3 numbers, the calculator determines the following:* Greatest Common Factor (GCF) using Factor Pairs* Rewrite Sum using the Distributive Property and factoring out the GCF* Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs* GCF using the method of Successive Division* GCF using the Prime Factorization method* Determine if the numbers are coprime and twin prime

Gregg has 8 cards.Half red,half black. He picks 2 cards from the deck.What is the probability both of them are red? Half means 4 cards are red and 4 cards are black. The first draw probability of red is: 4 total red cards out of 8 total cards = 4/8. [URL=' this is[/URL] 1/2 The second draw is 3 total red cards out of 7 remaining cards. Since 1 red was drawn (4 - 1) = 3 reds left and 1 card was drawn (8 -1) = left 3/7 Since each draw is independent, we multiply the probabilities: 1/2 * 3/7 = [B]3/14[/B]

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Guadalupe left the restaurant traveling 12 mph. Then, 3 hours later, Lauren left traveling the same direction at 24 mph. How long will Lauren travel before catching up with Guadalupe? Distance = Rate x Time Guadulupe will meet Lauren at the following distance: 12t = 24(t - 3) 12t = 24t - 72 [URL=' that equation into our search engine[/URL], we get: t = 6

gy=-g/v+w for g Multiply each side of the equation by v to eliminate fractions: gvy = -g + vw Add g to each side: gvy + g = -g + g + vw Cancel the g's on the right side and we geT: gvy + g = vw Factor out g on the left side: g(vy + 1) = vw Divide each side of the equation by (vy + 1): g(vy + 1)/(vy + 1) = vw/(vy + 1) Cancel the (vy + 1) on the left side and we geT: g = [B]vw/(vy + 1)[/B]

Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (Think of the monthly charges paid at the end of the month.) Enter the number of months it will take for the total cost for both gyms to be equal. Gym A cost function C(m) where m is the number of months: C(m) = Monthly charge * months + Joining Fee C(m) = 35m + 75 Gym B cost function C(m) where m is the number of months: C(m) = Monthly charge * months + Joining Fee C(m) = 60m Set them equal to each other: 35m + 75 = 60m To solve for m, [URL=' type this equation into our search engine[/URL] and get: m = [B]3[/B]

H minus 6 all cubed H minus 6 h - 6 All cubed means raise the entire expression to the 3rd power (h - 6)^3

Half of the difference of a and b The difference of a and b is written as: a - b Half of the difference means we divide (a - b) by 2: [B](a - b)/2[/B]

half of the sum of 2p and q The sum of 2p and q means we add q to 2p: 2p + q Half of this means we divide the sum by 2: [B](2p + q)/2[/B]

half of z increased by 10 Half of z (means we divide z by 2) z/2 Increased by 10 means we add 10 [B]z/2 + 10[/B]

half the difference of x and 3 The difference of x and 3 means we subtract 3 from x: x - 3 half of the difference means we divide the difference by 2: [B](x - 3)/2[/B]

half the sum of the numbers s, t, and u The [I]sum [/I]of s, t, and u means we add all 3: s + t + u [I]Half[/I] the sum means we divide the sum by 2: [B](s + t + u)/2[/B]

Free Half-Life of a Substance Calculator - Given a half-life (h) of a substance at time t, this determines the new substance size at time t_n, otherwise known as decay.

harley had $500 in his bank account at the beginning of the year. he spends $20 each week on food, clothing, and movie tickets. he wants to have more than $100 at the end of summer to make sure he has enough to purchase some new shoes before school starts. how many weeks, w, can harley withdraw money from his savings account and still have more than $100 to buy new shoes? Let the number of weeks be w. Harley needs $100 (or more) for shoes. We have the balance in Harley's account as: 500 - 20w >= 100 To solve this inequality for w, we [URL=' it in our search engine[/URL] and we get: [B]w <= 20[/B]

He charges $1.50 per delivery and then $2 per km he has to drive to get from his kitchen to the delivery address. Write an equation that can be used to calculate the delivery price and the distance between the kitchen and the delivery address. Use your equation to calculate the total cost to deliver to someone 2.4km away Let k be the number of kilometers between the kitchen and delivery address. Our Delivery equation D(k) is: [B]D(k) = 2k + 1.50[/B] The problem wants to know D(2.4): D(2.4) = 2(2.4) + 1.50 D(2.4) = 4.8 + 1.50 D(2.4) = [B]$6.30[/B]

Height and weight are two measurements used to track a child's development. The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender. In 2009, weights for all 80 cm girls in the reference population had a mean μ = 10.2 kg and standard deviation σ = 0.8 kg. Weights are normally distributed. X ~ N(10.2, 0.8). Calculate the z-scores that correspond to the following weights and interpret them. a. 11 kgb. 7.9 kgc. 12.2 kg a. [URL='" target="_blank']Answer A[/URL] - Z = 0.1 b. [URL=' B[/URL] - Z = -0.288 c. [URL=' C[/URL] - Z = 0.25

[B]I need 36 m of fencing for my rectangular garden. I plan to build a 2m tall fence around the garden. The width of the garden is 6 m shorter than twice the length of the garden. How many square meters of space do I have in this garden? List the answer being sought (words) ______Need_________________________ What is this answer related to the rectangle?_Have_________________________ List one piece of extraneous information____Need_________________________ List two formulas that will be needed_______Have_________________________ Write the equation for width_____________Have_________________________ Write the equation needed to solve this problem____Need____________________[/B]

[B]List the answer being sought (words) ______Area of the garden What is this answer related to the rectangle?_Have_________________________ List one piece of extraneous information____2m tall fence List two formulas that will be needed_______P = 36. P = 2l + 2w Write the equation for width_____________w = 2l - 6 Write the equation needed to solve this problem A = lw, P = 2l + 2w[/B]

Nick's age: x John's age: x/2 Pip's age = 2/3 * x/2 = x/3 The sum is 26, so we have: x + x/2 + x/3 = 26 Common denominator is (1 * 2 * 3) = 6 6x/6 + 3x/6 + 2x/6 = 26 Combine like terms: 11x/6 = 26 Cross multiply: 11x = 156 x = 14.1818 This doesn't make sense for age. Are you sure you wrote out the problem right?

Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took four tests. She scored 10 points better on the second test than she did on the first, 20 points better on the third test than on the first, and 30 points better on the fourth test than on the first. If the mean of these four tests was 70, what was her score on the third test? Givens: [LIST] [*]Let the first test score be s: [*]The second test score is: s + 10 [*]The third test score is: s + 20 [*]The fourth test score is: s + 30 [/LIST] The mean of the four tests is 70, found below: Sum of test scores / Number of Tests = Mean Plugging in our number, we get: (s + s + 10 + s + 20 + s + 30) / 4 = 70 Cross multiply and simplify: 4s + 60 = 70 * 4 4s + 60 = 280 To [URL=' this equation for s, we type it in our search engine[/URL] and we get: s = 55 So the third test score: s + 20 = 55 + 20 [B]75[/B]

Free Hexagon Calculator - This calculator solves for side length (s), Area (A), and Perimeter (P) of a hexagon given one of the 3 entries.

A candy vendor analyzes his sales records and ?nds that if he sells x candy bars in one day, his pro?t(in dollars) is given byP(x) = ? 0.001x2 + 3x ? 1800 (a.) Explain the signi?cance of the number 1800 to the vendor. (b.) What is the maximum pro?t he can make in one day, and how many candy bars must he sell to achieve it? I got 1800 as the amount he starts with, and can't go over. maximum pro?t as 4950 and if I got that right I am getting stuck on how to find how many candy bars. Thanks

a) 1800 is the cost to run the business for a day. To clarify, when you plug in x = 0 for 0 candy bars sold, you are left with -1,800, which is the cost of doing business for one day. b) Maximum profit is found by taking the derivative of the profit equation and setting it equal to 0. P'(x) = -0.002x + 3 With P'(x) = 0, we get: -0.002x + 3 = 0 Using our [URL=' solver[/URL], we get: x = 1,500 To get maximum profit, we plug in x = 1,500 to our [I]original profit equation[/I] P(1,500) = ? 0.001(1,500)^2 + 3(1,500) ? 1800 P(1,500) = -2,250 + 4,500 - 1,800 P(1,500) = $[B]450[/B]

how can you get 24 using only 8,8,3,3 [B]8/(3 - 8/3)[/B] since 3 = 9/3 9/3 - 8/3 = 1/3 8/1/3 = 24 [URL=' for this answer[/URL]:

How many cubic inches are in a cubic foot? Volume of a cube with 12 inch (1 foot sides) = 12 * 12 * 12 = [B]1728 cubic inches[/B]

How many dimes must be added to a bag of 200 nickels so that the average value of the coins in the bag is 8 cents? 200 nickels has a value of 200 * 0.05 = $10. Average value of coins is $10/200 = 0.05 Set up our average equation, where we have total value divided by total coins: (200 * 0.05 + 0.1d)/(200 + d) = 0.08 Cross multiply: 16 + 0.08d = 10 + 0.1d Using our [URL=' solver[/URL], we get: [B]d = 300[/B]

How many distinct 3 letter arrangements can be made using P, R, I, M and E? We have all unique letters. We want the combination formula 5 Choose 3, or C(5,3). Using our [URL=' calculator[/URL], we get 10 unique 3 letter arrangements.

How many hours are there in 720 minutes? 720 minutes * (1 hour / 60 minutes) = [B]12 hours[/B]

The tip off for this problem is the 2 phrases: [LIST] [*]circular table [*]arranged [/LIST] Whenever you see these 2 phrases together, the problem is asking for a [URL=' permutation[/URL] With n = 6: (6 - 1)! 5! 5 x 4 x 3 x 2 x 1 = [B]120 ways[/B] [MEDIA=youtube]4PXvg-UeN5Ao[/MEDIA]

how much are you paid by the minute if you get $170 a day? 170 / day * 1 day / 24 hours * 1 hour / 60 minutes 170 / (60*24) per minut 170 / 1440 [B]11.8 cents per minute[/B]

How much would you need to deposit in an account now in order to have $6000 in the account in 10 years? Assume the account earns 6% interest compounded monthly. We start with a balance of B. We want to know: B(1.06)^10 = 6000 B(1.79084769654) = 6000 Divide each side of the equation by 1.79084769654 to solve for B B = [B]3,350.37[/B]

How much would you need to deposit in an account now in order to have $6000 in the account in 15 years? Assume the account earns 8% interest compounded monthly. 8% compounded monthly = 8/12 = 0.6667% per month. 15 years = 15*12 = 180 months We want to know an initial balance B such that: B(1.00667)^180 = $6,000 3.306921B = $6,000 Divide each side by 3.306921 [B]B = $1,814.38[/B]

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I am thinking of a number. I multiply it by 14 and add 21. I get the same answer if I multiply by 4 and add 141. Let the number be n. We have two expressions: [LIST=1] [*]Multiply by 14 and add 21 is written as: 14n + 21 [*]Multiply by 4 and add 141 is written as: 4n + 141 [/LIST] The phrase [I]get the same expression[/I] means they are equal. So we set (1) and (2) equal to each other and solve for n: 14n + 21 = 4n + 141 [URL=' this equation into our search engine [/URL]to solve for n and we get: n = [B]12[/B]

I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13 and subtract 13.What is my number? Take a number (n): The first operation is multiply 5 times n, and then add 39: 5n + 139 The second operation is multiply 13 times n and subtract 13: 13n - 13 Set both operations equal to each other since they result in [I]the same number[/I] 5n + 139 = 13n - 13 [URL=' this equation into our search engine[/URL] and we get: [B]n = 19[/B]

I HAVE $11.60, all dimes and quarters, in my pocket. I have 32 more dimes than quarters. how many dimes, and how many quarters do i have? Let d = dimes and q = quarters. We have two equations: [LIST=1] [*]0.10d + 0.25q = 11.60 [*]d - q = 32 [/LIST] Set up a [URL=' of equations[/URL] to solve for d and q. [B]dimes (d) = 56 and quarters (q) = 24[/B] Check our work: 56 - 24 = 32 0.10(56) + 0.25(24) = $5.60 + $6.00 = $11.60

I have $36 dollars and it goes up by 3 every day how much money would I have after 500 days We have a balance function B(d) where d is the number of days passed since we first had $36: B(d) = 3d + 36 The problem asks for B(500): B(500) = 3(500) + 36 B(500) = 1500 + 36 B(500) = [B]1536[/B]

I have $789 in the bank and make 1% interest a month. How much money do I have at the end of 6 months? Our balance is found using our compound interest formula: New Balance = Starting Balance * (1 + i/100)^t With I = 1% and t = 6, we have: New Balance = 789 * (1 + 1/100)^6 New Balance = 789 * (1.01)^6 New Balance = 789 * 1.0615201506 New Balance = [B]837.54[/B]

I have 8 cookies. My friend at 7/10 of the 8 cookies. How many cookies did he have? 8 * (7/10) 56/10 Simplify by dividing the top and bottom by 2: [B]28/5 = 5.6 cookies[/B]

The simple interests earned on the sum of money for 4 years at 7.5% p.a. exceeds that on the same sum for 3.5 years at 8% p.a. by $90. (a)Find the original sum of money. (b)If the original sum of money accumulates to $4612.50 in 5 months at simple interest, find the interests rate per annum.

Simple interest = i(n) Using 4 years at 7.5% (0.075), we get: Simple interest = 4(0.075) = 0.3 What is p.a.?

If $9000 grows to $9720 in 2 years find the simple interest rate. Simple interest formula is Initial Balance * (1 + tn) = Current Balance We have [LIST] [*]Initial Balance = 9000 [*]Current Balance = 9720 [*]n = 2 [/LIST] Plugging in these values, we get: 9000 * (1 + 2t) = 9720 Divide each side by 9000 1 + 2t = 1.08 Subtract 1 from each sdie 2t = 0.08 Divide each side by 2 t = [B]0.04 or 4%[/B]

If (a - b)/b = 3/7, which of the following must also be true? A) a/b = -4/7 B) a/b = 10/7 C) (a + b)/b = 10/7 D) (a - 2b)/b = -11/7 We can rewrite (a - b)/b as: a/b - b/b = 3/7 Since b/b = 1, we have: a/b - 1 = 3/7 Since -1 = -7/7, we have: a/b - 7/7 = 3/7 Add 7/7 to each side: a/b - 7/7 + 7/7 = 3/7 + 7/7 Cancel the 7/7 on the left side, we get: [B]a/b = 10/7 or Answer B [MEDIA=youtube]PKjLuwoso1U[/MEDIA][/B]

If (x - 1)/3 = k and k = 2, what is the value of x? If k = 2, we have: (x - 1)/3 = 2 Cross multiply: x - 1 = 3 * 2 x - 1 = 6 [URL=' this equation into the search engine[/URL], we get: [B]x = 7[/B]

If 1/2 cup of milk makes 8 donuts. How much cups it takes to make 28 donuts? Set up a proportion of cups to donuts, where c is the number of cups required to make 28 donuts: 1/2/8 = c/28 Cross multiply: 28(1/2) = 8c 8c = 14 [URL=' this equation into our search engine[/URL], we get: [B]c = 1.75[/B]

If 11 times a number is added to twice the number, the result is 104 Let [I]the number[/I] be an arbitrary variable we call x. 11 times a number: 11x Twice the number (means we multiply x by 2): 2x The phrase [I]is added to[/I] means we add 2x to 11x: 11x + 2x Simplify by grouping like terms: (11 + 2)x = 13x The phrase [I]the result is[/I] means an equation, so we set 13x equal to 104: 13x = 104 <-- This is our algebraic expression To solve this equation for x, [URL=' type it in our search engine[/URL] and we get: x = [B]8[/B]

If 13,754 people voted for a politician in his first election, 15,420 voted for him in his second election, and 8,032 voted for him in the first and second elections, how many people voted for this politician in the first or second election? Let P(A) be the first election votes, P(B) be the second election votes, and P(A ? B) be votes for both the first AND the second elections. We want P(A U B). Use our [URL=' event calculator[/URL] P(A U B) = P(A) + P(B) - P(A ? B) P(A U B) = 13,754 + 15,420 - 8032 P(A U B) = 29,174 - 8,032 P(A U B) = [B]21,142[/B]

If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions. Convert 2 to a fraction with a denominator of 10: 20/2 = 10, so we multiply 2 by 10/10: 2*10/10 = 20/10 Add 2 to the numerator and denominator: (n + 2)/(d + 2) = 9/10 Cross multiply and simplify: 10(n + 2) = 9(d + 2) 10n + 20 = 9d + 18 Move constants to right side by subtracting 20 from each side and subtracting 9d: 10n - 9d = -2 Subtract 3 from the numerator and denominator: (n - 3)/(d - 3) = 4/5 Cross multiply and simplify: 5(n - 3) = 4(d - 3) 5n - 15 = 4d - 12 Move constants to right side by adding 15 to each side and subtracting 4d: 5n - 4d = 3 Build our system of equations: [LIST=1] [*]10n - 9d = -2 [*]5n - 4d = 3 [/LIST] Multiply equation (2) by -2: [LIST=1] [*]10n - 9d = -2 [*]-10n + 8d = -6 [/LIST] Now add equation (1) to equation (2) (10 -10)n (-9 + 8)d = -2 - 6 The n's cancel, so we have: -d = -8 Multiply through by -1: d = 8 Now bring back our first equation from before, and plug in d = 8 into it to solve for n: 10n - 9d = -2 10n - 9(8) = -2 10n - 72 = -2 To solve for n, we [URL=' this equation into our search engine[/URL] and we get: n = 7 So our fraction, n/d = [B]7/8[/B]

If 200 bacteria triple every 1/2 hour, how much bacteria in 3 hours Set up the exponential function B(t) where t is the number of tripling times: B(d) = 200 * (3^t) 3 hours = 6 (1/2 hour) periods, so we have 6 tripling times. We want to know B(6): B(6) = 200 * (3^6) B(6) = 200 * 729 B(6) = [B]145,800[/B]

If 2x + y = 7 and y + 2z = 23, what is the average of x, y, and z? A. 5 B. 7.5 C. 15 D. 12.25 Add both equations to get all variables together: 2x + y + y + 2z = 23 + 7 2x + 2y + 2z = 30 We can divide both sides by 2 to simplify: (2x + 2y + 2z)/2= 30/2 x + y + z = 15 Notice: the average of x, y, and z is: (x + y + z)/3 But x + y + z = 15, so we have: 15/3 = [B]5, answer A[/B] [MEDIA=youtube]tOCAhhfMCLI[/MEDIA]

If 3 coins are flipped simultaneously, the probability of having three tails is... The probability of flipping a head is 1/2. Since each coin flip is independent, we multiply the probabilities together of the three coin flips: P(HHH) = 1/2 * 1/2 * 1/2 P(HHH) = [B]1/8[/B]

If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3 Take this in pieces, where "a number" means an arbitrary variable, let's call it "x". [LIST=1] [*]3 times a number --> 3x [*]3 times a number added to 2 --> 3x + 2 [*]The number plus 4 --> x + 4 [*]is divided by --> (3x + 2)/(x + 4) [*]the result is 4/3 --> (3x + 2)/(x + 4) = 4/3 [/LIST]

If 3(c + d) = 5, what is the value of c + d? A) 3/5 B) 5/3 C) 3 D) 5 Divide each side of the equation by 3 to [U]isolate[/U] c + d 3(c + d)/3 = 5/3 Cancel the 3's on the left side, we get: c + d = [B]5/3, or answer B[/B]

If 3a+5b = 98 and a=11, what is the value of a +b a = 11: 3(11) + 5b = 98 33 + 5b = 98 Using our [URL=' solver[/URL], we get: b = 13 a + b = 11 + 13 a + b = [B]24[/B]

2 ways to do this: [B][U]Method 1[/U][/B] If 3r = 18, what is the value of 6r + 3? A) 6 B) 27 C) 36 D) 39 If [URL=' type in the equation 3r = 18 into our search engine[/URL], we get: r = 6 Take r = 6, and subtitute it into 6r + 3: 6(6) + 3 36 + 3 [B]39 or Answer D [U]Method 2:[/U][/B] 6r + 3 = 3r(2) = 3 We're given 3r = 18, so we have: 18(2) + 3 36 + 3 [B]39 or Answer D [MEDIA=youtube]ty3Nk2al1sE[/MEDIA][/B]

If 3x - y = 12, what is the value of 8^x/2^y We know 8 = 2^3 So using a rule of exponents, we have: (2^3)^x/2^y 2^(3x)/2^y Using another rule of exponents, we rewrite this fraction as: 2^(3x -y) We're given 3x - y = 12, so we have: [B]2^12[/B]

If 4 people have the same 7 shirts, what is the chance that they will wear the same shirt on one day? [LIST=1] [*]For each person, the probability they all wear the first shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the second shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the third shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the fourth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the fifth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the sixth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the seventh shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [/LIST] Now, we add up all those probabilities to get our answer, since any of the 7 scenarios above meets the criteria: (1 + 1 + 1 + 1 + 1 + 1 + 1)/256 [B]7/256[/B]

[SIZE=5]If 4(x-9)=3x-8x, what is x? [/SIZE] [SIZE=4]Multiply through: 4x - 36 = 3x - 8x Group like terms: 4x - 36 = -5x [/SIZE] [URL=' this equation into the search[/SIZE][/URL][SIZE=4][URL=' engine[/URL], we get: [B]x = 4[/B][/SIZE]

If 4x+7=xy-6, then what is the value of x, in terms of y Subtract xy from each side: 4x + 7 - xy = -6 Add 7 to each side: 4x - xy = -6 - 7 4x - xy = -13 Factor out x: x(4 - y) = -13 Divide each side of the equation by (4 - y) [B]x = -13/(4 - y)[/B]

If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integer. [LIST] [*]Let the integer be "x". [*]Square the integer: x^2 [*]7 times the square: 7x^2 [*]5 times the integer: 5x [*]Add them together: 7x^2 + 5x [*][I]The result is[/I] means an equation, so we set 7x^2 + 5x equal to 2 [/LIST] 7x^2 + 5x = 2 [U]This is a quadratic equation. To get it into standard form, we subtract 2 from each side:[/U] 7x^2 + 5x - 2 = 2 - 2 7x^2 + 5x - 2 = 0 [URL=' this problem into our search engine[/URL], and we get two solutions: [LIST=1] [*]x = 2/7 [*]x= -1 [/LIST] The problem asks for an integer, so our answer is x[B] = -1[/B]. [U]Let's check our work by plugging x = -1 into the quadratic:[/U] 7x^2 + 5x - 2 = 0 7(-1)^2 + 5(-1) - 2 ? 0 7(1) - 5 - 2 ? 0 0 = 0 So we verified our answer, [B]x = -1[/B].

If 800 feet of fencing is available, find the maximum area that can be enclosed. Perimeter of a rectangle is: 2l + 2w = P However, we're given one side (length) is bordered by the river and the fence length is 800, so we have: So we have l + 2w = 800 Rearranging in terms of l, we have: l = 800 - 2w The Area of a rectangle is: A = lw Plug in the value for l in the perimeter into this: A = (800 - 2w)w A = 800w - 2w^2 Take the [URL=' derivative[/URL]: A' = 800 - 4w Now set this equal to 0 for maximum points: 4w = 800 [URL=' this equation into the search engine[/URL], we get: w = 200 Now plug this into our perimeter equation: l = 800 - 2(200) l = 800 - 400 l = 400 The maximum area to be enclosed is; A = lw A = 400(200) A = [B]80,000 square feet[/B]

if a+b=2 and a2-b2=-4, what is the value of a-b? a^2 - b^2 = -4 Factor this: (a + b)(a - b) = -4 We know from above, (a +b) = 2, so substitute: 2(a - b) = -4 Divide each side by 2 [B](a - b) = -2[/B]

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A U B)=? We know the following formula for the probability of 2 events: P(A U B) = P(A) + P(B) - P(A intersection B) We're told A and B are independent, which makes P(A intersection B) = 0. So we're left with: P(A U B) = P(A) + P(B) - P(A intersection B) P(A U B) = 0.2 + 0.6 - 0 P(A U B) = [B]0.8[/B]

if a and b are odd then a + b is even Let a and b be positive odd integers of the form: [LIST] [*]a = 2n + 1 [*]b = 2m + 1 [/LIST] a + b = 2n + 1 + 2m + 1 a + b = 2n + 2m + 1 + 1 Combing like terms, we get: a + b = 2n + 2m + 2 a + b = 2(n + m) + 2 Let k = n + m a + b = 2k + 2 [B]Therefore a + b is even[/B]

if a city grows by 12% per month what is the yearly growth rate We know that there are 12 months in a year. 12% = 0.12 Annual Growth Rate = (1 + Monthly Growth Rate)^12 - 1 Annual Growth Rate = (1 + 0.12)^12 - 1 Annual Growth Rate = (1.12)^12 - 1 Annual Growth Rate = 3.89597599255 - 1 Annual Growth Rate = 2.90 For our percentage, our annual growth rate is the Annual growth rate * 100% 2.90 * 100% = [B]290%[/B]

If a die is rolled, what is the probability that the number rolled will not be a "5"? Possible rolls: {1, 2, 3, 4, 5, 6} Probability of not a 5 means: {1, 2, 3, 4, 6} P(Not 6) = 1 - P(6) P(Not 6) = 1 - 1/6 P(Not 6) = [B]5/6[/B]

if a divides b, then a divides bc Suppose a divides b. Then there exists an integer q such that b = aq, so that bc = a(qc) and a divides bc. Suppose that a divides c. Then there exists an integer k such that c = ak, so that bc = a(kb) and a divides bc.

If a is an even integer and b is an odd integer then prove a ? b is an odd integer Let a be our even integer Let b be our odd integer We can express a = 2x (Standard form for even numbers) for some integer x We can express b = 2y + 1 (Standard form for odd numbers) for some integer y a - b = 2x - (2y + 1) a - b = 2x - 2y - 1 Factor our a 2 from the first two terms: a - b = 2(x - y) - 1 Since x - y is an integer, 2(x- y) is always even. Subtracting 1 makes this an odd number. [MEDIA=youtube]GDVuQ7bGHx8[/MEDIA]

if a number is added to its square, it equals 20. Let the number be an arbitrary variable, let's call it n. The square of the number means we raise n to the power of 2: n^2 We add n^2 to n: n^2 + n It equals 20 so we set n^2 + n equal to 20 n^2 + n = 20 This is a quadratic equation. So [URL=' type this equation into our search engine[/URL] to solve for n and we get two solutions: [B]n = (-5, 4)[/B]

If a number is decreased by 5, and then the result is multiplied by 2, the result is 26 The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x [I]Decreased by[/I] means we subtract 5 from x: x - 5 Multiply the result by 2: 2(x - 5) The result is 26 means we set 2(x - 5) equal to 26: [B]2(x - 5) = 26[/B]

If a number is increased by 16 and then divided by 3, the result is 8. Let x be the number. We have: (x + 16)/3 = 8 Cross multiply x + 16 = 24 Using our equation calculator, we get: [B]x = 8[/B]

If a person from Septon at .1 of their cookie, what fraction of the cookie did they eat using base 10 (1/7)^1 = 1/7

If a speedometer indicates that a car is traveling at 65 kilometers per hour, how fast is the car traveling in miles per hour? (Round to the nearest tenth.) Set up a proportion of miles per kilometers: 0.621/1 = n/65 Using our [URL=' calculator,[/URL] we get: n = [B]40.365[/B]

If a universal set contains 250 elements, n(A) = 90, n(B) = 125, and n(A ? B) = 35, find n(A ? B)'. We know from set theory that: n(A U B) = n(A) + n(B) - n(A ? B) Plugging in our given values, we get: n(A U B) = 90 + 125 - 35 n(A U B) = 180 The problem asks for n(A U B)'. This formula is found with: n(A U B)' = n(U) - n(A U B) n(U) is the universal set which is 250, so we have: n(A U B)' = 250 - 180 n(A U B)' = [B]70[/B]

If a+b=16, then what is 3a+3b= Factor 3a + 3b: 3(a + b) Since we know a+b = 16, we have: 3(16) = [B]48[/B]

If a, b, and c are positive integers such that a^b = x and c^b = y, then xy = ? A) ac^b B) ac^2b C) (ac)^b D) (ac)^2b E) (ac)^b^2 xy = a^b * c^b We can use the Power of a Product Rule a^b * c^b = (ac)^b Therefore: xy = [B](ac)^b - Answer C[/B]

If a/b = 2, what is the value of 4b/a? 4b/a = 4(b/a) If a/b = 2, then the reciprocal b/a = 1/2. So we have 4(1/2) = [B]2[/B]

If a=-9 and b=-6, show that (a-b) unequal (b-a) [U]a - b:[/U] a - b = -9 - -6 a - b = -9 + 6 a - b = -3 [U]b - a:[/U] b - a = -6 - -9 b - a = -6 + 9 b - a = 3 [B]Since -3 <> 3, then a - b <> b - a[/B]

If an employee starts saving with $750 and increases his savings by 8% each month, what will be his total savings after 10 months? Set up the savings function S(m), where m is the number of months and I is the interest rate growth: S(m) = Initial Amount * (1 + i)^m Plugging in our number at m = 10 months we get: S(10) = 750 * (1 + 0.08)^10 S(10) = 750 * 1.08^10 S(10) = [B]$1,619.19[/B]

If approximately 68% of the scores lie between 40.7 and 59.9 , then the approximate value of the standard deviation for the distribution, according to the empirical rule, is The empirical rule states 68% of the values lie within 1 standard deviation of the mean. The mean is the midpoint of the interval above: (59.9 + 40.7)/2 = 50.3 Standard deviation is the absolute value of the mean - endpoint |59.9 - 50.3| = [B]9.6[/B]

if a^b=x and c^b=y then xy=? xy = a^b * c^b xy = [B](ac)^b[/B]

if ballons are on sale at 15 for$3, whats the cost for a ballon? a)50cents b)25cost c)20cents d)20 dollars Let c be the cost of 1 balloon. We set up a proportion of balloons to cost: 15/3 = 1/c To solve this proportion for c, we [URL=' it in our search engine[/URL] and we get: c = [B]0.2 or 20 cents[/B]

If Bill's salary is $25 and he gets a 20 commission on every newspaper he sells, how many must he sell to make $47 Set up bills Earnings function E(n) where n is the number of newspapers he sells: E(n) =. Cost per newspaper * number of newspapers sold + base salary E(n) = 0.2n + 25 We're asked to find n when E(n) = 47, so we set E(n) = 47 and solve for n: 0.2n + 25 = 47 Using our [URL=' solver[/URL], we get: n = [B]110[/B]

If c=3 and d=4 evaluate cd divided by 2 cd = 3(4) cd = 12 Divide this by 2: 12/2 [B]6[/B]

If Distance equals Speed times Time (D = S x T), then what does time equal in terms of speed and distance? Divide each side by S to isolate T: D/S = S x T/S Cancel the S's on the right side: [B]T = D/S[/B]

If Ef = 3x,Fg = 2x,and EG = 5 By segment addition, we have: EF + FG = EG 3x + 2x = 5 To solve for x, we t[URL=' this equation into our math engine [/URL]and we get: x = 1 So EF = 3(1) = [B]3[/B] FG = 2(1) = [B]2[/B]

If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG? By segment addition, we know that: EF + FG = EG Substituting in our values for the 3 segments, we get: 9x - 17 + 17x - 14 = 20x + 17 Group like terms and simplify: (9 + 17)x + (-17 - 14) = 20x - 17 26x - 31 = 20x - 17 Solve for [I]x[/I] in the equation 26x - 31 = 20x - 17 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 26x and 20x. To do that, we subtract 20x from both sides 26x - 31 - 20x = 20x - 17 - 20x [SIZE=5][B]Step 2: Cancel 20x on the right side:[/B][/SIZE] 6x - 31 = -17 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -31 and -17. To do that, we add 31 to both sides 6x - 31 + 31 = -17 + 31 [SIZE=5][B]Step 4: Cancel 31 on the left side:[/B][/SIZE] 6x = 14 [SIZE=5][B]Step 5: Divide each side of the equation by 6[/B][/SIZE] 6x/6 = 14/6 x = [B]2.3333333333333[/B]

If Emma reads 1 page of a book in 44 seconds, how many pages will she read in 15 minutes Convert 15 minutes to seconds: 15 minutes = 60 * 15 = 900 seconds Set up a proportion of pages read to seconds where p is the number of pages read in 900 seconds (15 minutes): 1/44 = p/900 [URL=' this proportion into our search engine[/URL], we get: p = [B]20.45[/B]

If f(1) = 2 and f(n) = nf(n-1)+4 then find the value of f(4) Find f(2) f(2) = 2*f(2 - 1) + 4 f(2) = 2*f(1) + 4 f(2) = 2*2 + 4 f(2) = 4 + 4 f(2) = 8 Find f(3) f(3) = 2*f(3 - 1) + 4 f(3) = 2*f(2) + 4 f(3) = 2*8+ 4 f(3) = 16 + 4 f(3) = 20 Find f(4) f(4) = 2*f(4 - 1) + 4 f(4) = 2*f(3) + 4 f(4) = 2*20+ 4 f(4) = 40 + 4 f(3) = [B]44[/B]

If f(x) = (3x + 7)^2, then f(1) = ? A) 10 B) 16 C) 58 D) 79 E) 100 f(1) = (3(1) + 7)^2 f(1) = (3 + 7)^2 f(1) = 10^2 [B]f(1) = 100 - Choice E[/B]

If f(x) = 3 - 2x and g(x) = 1/x + 5 what is the value of (f/g)(8)? Set up (f/g)(x) (3 - 2x)/(1/x + 5) Now find (f/g)(8) (3 - 2(8))/(1/8+ 5) (3 - 16)/(5.125) -13/5.125 [B]2.5366[/B]

If f(x) = 3x + 1 and g(x) = x^2 + 2x, find x when f(g(x)) = 10 [U]Evaluate f(g(x))[/U] f(g(x)) = 3(x^2 + 2x) + 1 f(g(x)) = 3x^2 + 6x + 1 [U]When f(g(x)) = 10, we have[/U] 10 = 3x^2 + 6x + 1 [U]Subtract 10 from each side:[/U] 3x^2 + 6x - 9 = 0 Divide each side of the equation by 3 x^2 + 2x - 3 = 0 Factor, we have: (x + 3)(x - 1) = 0 So x is either [B]1 or -3[/B]

If f(x) = ax^2 + bx + c and f(0) = 1 and f(-1) = 3, what is a - b Evaluate f(0) f(0) = a(0^2) + b(0) + c f(0) = a(0) + b(0) + c f(0) = c Since f(0) = 1, we have c = 1 Evaluate f(-1) f(-1) = a(-1^2) + b(-1) + c f(-1) = a(1) - b + c f(-1) = a - b + c Since f(-1) = 3, we have: a - b + c = -3 We learned above that f(0) = 1, so c = 1. Plug c = 1 into f(-1) a - b + 1 = -3 Subtract 1 from each side: a - b + 1 - 1 = -3 - 1 Cancel the 1's on the left side and we get: a - b = [B]-4[/B]

if f(x)=-5x+11 and f(n)=21 what does n equal f(n) = -5(n) + 11 Since f(n) = 21, we have: -5(n) + 11 = 21 Using our [URL=' solver[/URL], we get [B]n = -2[/B].

If f={(4,2),(5,1),(6,2),(7,3),(8,6)} then the range of f is what The range is the full set of all possible y-values: {1, 2, 2, 3, 6} Remove duplicates, we get: [B]{1, 2, 3, 6}[/B]

If FG = 9, GH = 4x, and FH = 7x, what is GH? By segment addition, we have: FG + GH = FH Substituting in the values given, we have: 9 + 4x = 7x To solve this equation for x, we [URL=' it in our math engine[/URL] and we get: x = 3 The question asks for GH, so with x = 3, we have: GH = 4(3) GH = [B]12[/B]

If FG=11, GH=x-2, and FH=3x-11, what is FH By segment addition, we have: FG + GH = FH 11 + x - 2 = 3x - 11 To solve this equation for x, we [URL=' it in or math engine[/URL] and we get: x = 10 FH = 3x - 11. So we substitute x = 10 into this: FH = 3(10) - 11 FH = 30 - 11 FH = [B]19[/B]

if flip a coin 4 times, what is the probability of getting all 4 tails. P(Tails) = 1/2 Each flip is independent, so we have: [URL='(TTTT)[/URL] = [B]1/16[/B]

If Franks age is double of Willis age and the sum of their ages is 42. What are their ages? Let Frank's age be f. Let Willis's age be w. We're given two equations: [LIST=1] [*]f = 2w <-- Double means multiply by 2 [*]f + w = 42 [/LIST] Substitute equation (1) into equation (2): 2w + w = 42 To solve for w, [URL=' this equation into our search engine[/URL]. We get: w = [B]14 [/B] Now, take w = 14, and substitute it back into equation (1) to solve for f: f = 2(14) f = [B]28[/B]

if g(x) =5x + 3 and g(a) = 14, then what is the value of a? We set g(a) = 5a + 3 = 14 5a + 3 = 14 Using our [URL=' solver[/URL], we get: a = [B]2.2[/B]

If H = {(1,-4), (2,-3), (3,-2), (4,-1),...), What is H(9)? It looks like each x-coordinate goes up by 1 and each y-coordinate decreases by 1. Their difference is 5. So we have: H(9) = [B](9, 4)[/B]

if hose a can fill up a swimming pool in 6 hours, hose b in 3 hours, hose c in 2 hours, how long will it take to fill up the pool using all 3 hoses? Let V be the pool's Volume. Each hour, the hoses fill up this much of the pool: [LIST] [*]Hose A, V/6 of the pool [*]Hose B, V/3 of the pool [*]Hose C, V/2 of the pool [/LIST] Effective fill rate is: V/6 + V/3 + V/2 6V/36 + 12V/36 + 18V/36 36V/36 which is volume units per hour Let t = units / rate t = 1 hour, so we have: t = units / rate t = V (volume units) / V (volume units / hour) t = [B]1 hour[/B]

if i = square root of -1 what is the sum (7 + 3i) + (-8 + 9i) We group like terms, and we get: 7 - 8 + (3 + 9)i Simplifying, we get: [B]-1 + 12i[/B]

If I add 8 to the number and then multiply the result by 6 I get the same answer as when I add 58 to a number. Form an equation Let the number be n. We're given: 6(n + 8) = n + 58 Multiply through: 6n + 48 = n + 58 To solve this equation for n, [URL=' type it into our search engine[/URL] and we get: n = [B]2[/B]

If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it take me to read 58 pgs? Set up a proportion, of reading time to pages where m is the number of minutes it takes you to read 58 pages. 2 hours and 30 minutes is: 60(2) + 30 120 + 30 150 minutes Our proportion is: 150/93.25 = m/58 [URL=' this proportion into the search engine[/URL], and we get: [B]m = 93.3 minutes, or about 1 hour, 33 minutes[/B]

If I make 40,000 dollars every 15 minutes then how long will it take me to make a million Let f be the number of fifteen minute blocks. We're given: 40000f = 1000000 To solve for f, we [URL=' this equation into our search engine[/URL] and we get: f = 25 Total minutes = Fifteen minute blocks (f) * 15 minutes Total minutes = 25 * 15 Total minutes = [B]375 minutes or 6 hours and 15 minutes[/B]

If Jody had $3 more she would have twice as much as Lars together they have $60. Let j be Jody's money and l be Lars's money. We have two equations: [LIST=1] [*]j + l = 60 [*]j + 3 = 2l [/LIST] Rearrange (2) to solve for j by subtracting 3 j = 2l - 3 Now substitute this into (1) (2l - 3) + l = 60 Combine like terms 3l - 3 = 60 Enter this into our [URL=' calculator[/URL], and we get: [B]l = 21[/B] Now plug l = 21 into our rearranged equation above: j = 2(21) - 3 j = 42 - 3 [B]j = 39[/B]

If labor (x) costs $249 per unit, materials (y) cost $162 per unit, and capital (z) costs $ 77 per unit, write a function for total cost. Total Cost = Labor Total Cost + Materials Total Cost + Capital Total Cost Total Cost = [B]249x + 162y + 77z[/B]

if Logb(5)=3.56 and logb(8)=4.61 then what is logb(40) There exists a logarithmic identity which says log(xy) = log(x) + log(y). Since the two logs above have the same base b, we have: x = 5 and y = 8. So we have: logb(40) = logb(5) + logb(8) logb(40) = 3.56 + 4.61 logb(40) = [B]8.17[/B]

if m is odd and n is odd, then mn is odd. m = 2k +a where a = 0 or 1 n = 2l + b where b = 0 or 1 mn = (2k + a)(2l + b) = 4kl + 2kb + 2al + ab Since mn is odd, ab = 1 since a = 1 and b = 1

If m% of m is 36, then m is? m% = m/100, so we have: m/100 * m = 36 m^2/100 = 36 Cross multiply and we get: m^2 = 3600 We use our [URL='(3600%2F1)&pl=Simplify+Radical+Expression']radical expressions simplifier[/URL] to get: m = [B]60 [MEDIA=youtube]vlsIbZz4dx4[/MEDIA][/B]

If Mr hernandez has 5 times as many students as Mr daniels and together they have 150 students how many students do each have? Let h = Mr. Hernandez's students and d = Mr. Daniels students. We are given two equations: (1) h = 5d (2) d + h = 150 Substitute equation (1) into equation (2) d + (5d) = 150 Combine like terms: 6d = 150 Divide each side of the equation by 6 to isolate d d = 25 <-- Mr. Daniels Students Now, plug the value for d into equation (1) h = 5(25) h = 125 <-- Mr. Hernandez students

Look at the Contrapositive: If n is even, then 3n + 2 is even... Suppose that the conclusion is false, i.e., that n is even. Then n = 2k for some integer k. Then we have: 3n + 2 = 3(2k) + 2 3n + 2 = 6k + 2 3n + 2 = 2(3k + 1). Thus 3n + 2 is even, because it equals 2j for an integer j = 3k + 1. So 3n + 2 is not odd. We have shown that (n is odd) ? (3n + 2 is odd), therefore, the contrapositive (3n + 2 is odd) ? (n is odd) is also true.

if n(A) = 6, n(A intersect B) = 2 and n(A union B) = 11, find n(B). n(A union B) = n(A) + n(B) - n(A intersect B) Plugging in our given values, we have: 11 = 6 + n(B) - 2 11 = 4 + n(B) Subtract 4 from each side: [B]n(B) = 7[/B]

If n(A)=1200, n(B)=1250 and n(AintersectionB)=320, then n(AUB) is We know that: n(AUB) = n(A) + n(B) - n(AintersectionB) Plugging in our given numbers, we get: n(AUB) = 1200 + 1250 - 320 n(AUB) = [B]2130[/B]

If one calculator costs d dollars, what is the cost, in dollars, of 13 calculators? Set up cost function C(n), where n is the number of calculators: C(n) = dn C(13) = [B]13d[/B]

If one half of a number is 24, what is twice the number? Let the number be n. We have: n/2 = 24 Cross multiply, we get n = 48 The problem asks for 2n. 2(48) = [B]96[/B]

If p = log2(x), what is the value of log2(2x^3) in terms of p? A. 6p B. 2p^3 C. 1 + 3p D. 3 + 3p E. 1 + p^3 log2(2x^3) = log2(2) + log2(x^3) log2(2) = 1, so we have: log2(2x^3) = 1 + 3log2(x) Since we're given log2(x) = p, we have: log2(2x^3) = [B]1 + 3p - Answer C [MEDIA=youtube]-fEkVno3bxs[/MEDIA][/B]

If p is inversely proportional to the square of q, and p is 2 when q is 4, determine p when q is equal to 2. We set up the variation equation with a constant k such that: p = k/q^2 [I](inversely proportional means we divide) [/I] When q is 4 and p is 2, we have: 2 = k/4^2 2 = k/16 Cross multiply: k = 2 * 16 k = 32 Now, the problem asks for p when q = 2: p = 32/2^2 p = 32/4 p = [B]8 [MEDIA=youtube]Mro0j-LxUGE[/MEDIA][/B]

If p+4=2 and q-3=2, what is the value of qp? Isolate p by subtracting 4 from each side using our [URL=' calculator[/URL] p = -2 Isolate q by adding 3 to each side using our [URL=' calculator[/URL]: q = 5 pq = (-2)(5) [B]pq = -10[/B]

If QR = 16, RS = 4x ? 17, and QS = x + 20, what is RS? From the segment addition rule, we have: QR + RS = QS Plugging our values in for each of these segments, we get: 16 + 4x - 17 = x + 20 To solve this equation for x, [URL=' type it in our search engine[/URL] and we get: x = 7 Take x = 7 and substitute it into RS: RS = 4x - 17 RS = 4(7) - 17 RS = 28 - 17 RS = [B]11[/B]

If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how many of each coin does he have? Using q for quarters and n for nickels, and using 525 cents as $5.25, we're given two equations: [LIST=1] [*]q = 4n [*]0.25q + 0.05n = 5.25 [/LIST] Substitute equation (1) into equation (2) for q: 0.25(4n) + 0.05n = 5.25 Multiply through and simplify: n + 0.05n = 5.25 To solve this equation for n, we [URL=' it in our search engine[/URL] and we get: n = [B]5 [/B] To get q, we plug in n = 5 into equation (1) above: q = 4(5) q = [B]20[/B]

if sc = hr and hr=ab then sc=ab sc = hr (given) Since hr = ab, we can substitute ab for hr by substitution: [B]sc = ab[/B]

If sin(26)=x what does cos(64) equal? Using our cofunction calculator, we see the cofunction of sin(26) = cos(64). Therefore, sin(26) = cos(64), so cos(64) = [B]x[/B]

If tanx = 3/4 ,what is cosx? tan(x) = sin(x)/cos(x), so we have: sin(x)/cos(x) = 3/4 cross multiply: 4sin(x) = 3cos(x) Divide each side by 3 to isolate cos(x): cos(x) = [B]4sin(x)/3 [/B]

If the circumference of a circular rug is 16? feet, then what is the area of the rug in terms of pi C = 2pir, so we have: C = 16? 16? = 2?r Divide each side by 2?: r = 16?/2? r = 8 Now, the area of a circle A is denoted below: A = ?r^2 Given r = 8 from above, we have: A = ?(8)^2 A = [B]64?[/B]

Let a be the cost of the ball and b be the cost of the bat: We're given 2 equations: [LIST=1] [*]a + b = 1.10 [*]b = a + 1 [/LIST] Substitute equation (2) into equation (1) for b: a + a + 1 = 1.10 Combine like terms: 2a + 1 = 1.10 Subtract 1 from each side: 2a + 1 - 1 = 1.10 - 1 2a = 0.10 Divide each side by 2: 2a/2 = 0.10/2 a = [B]0.05[/B] [MEDIA=youtube]79q346Hy7R8[/MEDIA]

If the diameter of a circle is n, what is the circumference? Diameter of a circle = pi(d) Given d = n, we have: Diameter = pi(n)

If the difference of a number and 4 is multiplied by 3 the result is 19 The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x The difference of a number and 4: x - 4 The phrase [I]is multiplied by[/I] means we multiply x - 4 by 3: 3(x - 4) The phrase [I]the result is[/I] means equals, so we set 3(x - 4) equal to 19 [B]3(x - 4) = 19 [MEDIA=youtube]Q8bnVJuWeVk[/MEDIA][/B]

If the equation of a line passes through the points (1, 3) and (0, 0), which form would be used to write the equation of the line? [URL=' (1,3),(0,0) into the search engine[/URL], we get a point-slope form: [B]y - 3 = 3(x - 1)[/B] If we want mx + b form, we have: y - 3 = 3x - 3 Add 3 to each side: [B]y = 3x[/B]

if the input is 3 and the output is 13 We write this as: [B]f(3) = 13[/B]

If the max time that John can spend on Client A ($20/hr) in one week is 32 hours, and the min time is 8 hours, while the max time on Client B ($14/hr) is 8 hours and the min 5 hours, what is the RANGE (max, min) of total pay he can earn in one week (40 hours) [LIST] [*]Client A Minimum = 20 x 8 hours = $160 [*]Client A Maximum = 20 x 32 hours = $640 [*]Client B Minimum = 14 x 5 hours = $70 [*]Client B Maximum = 14 x 8 hours = $112 [/LIST] [U]The Total Maximum Pay is found by adding Client A Maximum and Client B Maximum[/U] Total Maximum = Client A Maximum + Client B Maximum Total Maximum = 640 + 112 Total Maximum = 752 [U]The Total Minimum Pay is found by adding Client A Minimum and Client B Minimum[/U] Total Minimum = Client A Minimum + Client B Minimum Total Minimum = 160 + 70 Total Minimum = 230 [U]The Range is the difference between the Total maximum and the Total minimum[/U] Range(Total Maximum, Total Minimum) = Total Maximum - Total Minimum Range(752, 230) = 752 - 230 Range(752, 230) = [B]522[/B]

If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide must the field be? The perimeter of a rectangle P, is denoted as: P = 2l + 2w We're given l = 25, and P = 120, so we have 2(25) + 2w = 120 Simplify: 2w + 50 = 120 [URL=' this equation into our search engine[/URL], we get: [B]w = 35[/B]

If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, then what are the length and width? The perimeter (P) of a rectangle is: 2l + 2w = P We're given P = 44, so we substitute this into the rectangle perimeter equation: 2l + 2w = 44 We're also given w = 0.5l - 2. Substitute the into the Perimeter equation: 2l + 2(0.5l - 2) = 44 Multiply through and simplify: 2l + l - 4 = 44 Combine like terms: 3l - 4 = 44 [URL=' this equation into the search engine[/URL], and we get: [B]l = 16[/B] Substitute this back into the equation w = 0.5l - 2 w = 0.5(16) - 2 w = 8 - 2 [B]w = 6[/B]

if the point (.53,y) is on the unit circle in quadrant 1, what is the value of y? Unit circle equation: x^2 + y^2 = 1 Plugging in x = 0.53, we get (0.53)^2 + y^2 = 1 0.2809 + y^2 = 1 Subtract 0.2809 from each side: y^2 = 0.7191 y = [B]0.848[/B]

If the probability of getting struck by lighting each year is 1 in 1,000,000, what is the probability that you will not be struck by lightning in one year? Our sample space is either getting struck by lightning or NOT getting struck by lightning. So we have: P(Not getting struck by lightning) = 1 - P(Getting struck by lightning) P(Not getting struck by lightning) = 1 - 1/1,000,000 P(Not getting struck by lightning) = [B]999,999/1,000,000[/B]

If the probability of rain is 15%, what is the probability that it won't rain? If we assign the probability of raining as event A, then A' (A complement) is the probability it won't rain. Since it either rains or doesn't rain are the only two events. There exists an axiom in statistics that states: P(A) + P(A') = 1 Rearranging this, we get: P(A') = 1 - P(A) If we assign the probability of raining as event A which is 0.15, we get: P(A') = 1 - 0.15 P(A') = [B]0.85[/B]

If the probability of winning is X, what is the probability of losing? (Assume there are no ties.) This means you can either win or lose. Since all probabilities in the sample space must add up to 1, then we have: P(Winning) + P(Losing) = 1 P(Losing) = 1 - P(Winning) Since P(Winning) = X, we have: P(Losing) = [B]1 - X[/B]

If the ratio of private school students to public school students in a city is 4 to 15 and there is a total of 18,601 students, how many students are in public schools? Since 4 out of 15 are public school students, this means (15 - 4)/15 = 11/15 are public school students. The total public school students are (11/15) * 18601 = 13,640.73. Rounded up, it is [B]13,641[/B].

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find the time taken by aeroplane to cover 1200m initially. We know from the distance formula (d) using rate (r) and time (t) that: d = rt Regular speed: 1200 = rt Divide each side by t, we get: r = 1200/t Reduced speed. 20 minutes = 60/20 = 1/3 of an hour. So we multiply 1,200 by 3 3600 = (r - 40)(t + 1/3) If we multiply 3 by (t + 1/3), we get: 3t + 1 So we have: 3600 = (r - 40)(3t + 1) Substitute r = 1200/t into the reduced speed equation: 3600 = (1200/t - 40)(3t + 1) Multiply through and we get: 3600 = 3600 - 120t + 1200/t - 40 Subtract 3,600 from each side 3600 - 3600 = 3600 - 3600 - 120t + 1200/t - 40 The 3600's cancel, so we get: - 120t + 1200/t - 40 = 0 Multiply each side by t: -120t^2 - 40t + 1200 = 0 We've got a quadratic equation. To solve for t, [URL=' type this in our search engine[/URL] and we get: t = -10/3 or t = 3. Since time [I]cannot[/I] be negative, our final answer is: [B]t = 3[/B]

if the vertex of a parabola is (4,9) what is the axis of symmetry [B]x = 4[/B]

If there are 10^30 grains of sand on Beach A, how many grains of sand are there on a beach the has 10 times the sand as Beach A? (Express your answer using exponents.) 10^30 * 10 = 10^(30 + 1) = [B]10^31[/B]

If two coins are flipped, what is the probability that there will not be two heads? There's only one way to flip 2 coins and get 2 heads: P(HH) = 1/2 * 1/2 = 1/4 Which means the probability of NOT getting 2 heads is: 1 - 1/4 = [B]3/4 [MEDIA=youtube]vNbA7vE361M[/MEDIA][/B]

If two consecutive even numbers are added, the sum is equal to 226. What is the smaller of the two numbers? Let the smaller number be n. The next consecutive even number is n + 2. Add them together to equal 226: n + n + 2 = 226 Solve for [I]n[/I] in the equation n + n + 2 = 226 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 1)n = 2n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2n + 2 = + 226 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 2 and 226. To do that, we subtract 2 from both sides 2n + 2 - 2 = 226 - 2 [SIZE=5][B]Step 4: Cancel 2 on the left side:[/B][/SIZE] 2n = 224 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2n/2 = 224/2 n = [B]112 [URL='

If V is the volume of a cube whose side is s, express s in terms of V: We know the Volume (V) of a cube with side length s is: V = s^3 Take the cube root of each side: V^1/3 = (s^3)^1/3 s = [B]V^1/3[/B]

If x = 2y/3 and y = 18, what is the value of 2x - 3? A) 21 B) 15 C) 12 D) 10 Substitute the values into the equation: 2(2y/3) - 3 <-- Given x = 2y/3 Simplifying, we have: 4y/3 - 3 Now substitute y = 18 into this: 4(18)/3 - 3 4(6) - 3 24 - 3 [B]21 or Answer A[/B]

If x represents the first, or the smaller, of two consecutive odd integers, express the sum of the two integers in terms of x If x is the first of two consecutive odd integers, then we find the next consecutive odd integer by adding 2 to x: x + 2 The sum of the two consecutive odd integers is expressed by x + (x + 2) Simplify by grouping like terms, we get: [B]2x + 2[/B]

If x varies directly with y and x = -3 when y = 12, what is the constant of variation? Using our [URL=' calculator[/URL], we see the constant of variation (k) is: k =[B] -1/4 or -0.25[/B]

If x/2y = 3/4, what is the value of y/x? Cross multiply this proportion: 4x = 3(2y) 4x = 6y Divide each side by x: 4x/x = 6y/x The x's cancel, and we have: 6y/x = 4 Divide each side by 6: 6y/6x = 4/6 The 6's on the left cancel, we have: y/x = 4/6 We can simplify this. [URL=' in Simplify 4/6 into the search engine[/URL], and we get 2/3. y/x = [B]2/3[/B]

If you are running 6 miles per hour, then it takes you 10 minutes to run 1 mile. If you are running 8 miles per hour, it takes you 7.5 minutes to run a mile. What does your speed have to be for your speed in miles per hour to be equal to your mile time in minutes? From above, we have: [LIST] [*]6mph x 10 minutes = 1 mile [*]8mph x 7.5 minutes = 1 mile [/LIST] Notice that mph x minutes = 60 since there are 60 minutes in 1 hour? So we have x mph x y minutes = 60. Since we want mph and y (minutes) = x (mph), we have x^2 = 60 x = sqrt(60) [B]x = 7.746 mph[/B]

if you buy 50 bales of hay at $3.56 each, and then buy an additional 234 bales at $3.33 each, how much do you pay for the entire lot of 284 bales? Since cost = price * quantity, we have: Total lot cost = price(1) of hay * bales(1) of hay + price(2) of hay * bales(2) of hay Total lot cost = 3.56 * 50 + 3.33 * 24 Total lot cost = 178 + 79.92 Total lot cost = [B]257.92[/B]

If you can buy 1?3 of a box of chocolates for 6 dollars, how much can you purchase for 4 dollars? Write your answer as a fraction of a box. Set up a proportion of dollars to boxes where b is the number of boxes for $4: 6/1/3 = 4/b Cross multiply: 6b = 4/3 Multiply each side by 1/6 to isolate b: b = 4/18 [URL=' in GCF(4,18) into the search engine[/URL]. We get a greatest common factor of 2. Divide 4 and 18 in the fraction by 2. We get the reduced fraction of: [B]b = 2/9[/B]

if you have a bag with 7 red balls in it and 3 yellow balls in it, whats the probability of pulling out a yellow ball P(Yellow) = 3/(3 + 7) P(Yellow) = [B]3/10 or 0.3[/B].

If you put $1 a day away and every day you add a dollar to the previous days amount, how much would you have after 100 days Day 1, you have 1 Day 2, you have 1 + 1 = 2 Day 3, you have 1 + 2 = 3 So our formula for day n is: D(n) = n D(100) = [B]100[/B]

If you take a Uber and they charge $5 just to show up and $1.57 per mile, how much will it cost you to go 12 miles? (Assume no tip.) a. Create an equation from the information above. b. Identify the slope in the equation? c. Calculate the total cost of the ride? 2. With the same charges as #1, how many miles could you go with $50, if you also gave a $7.50 tip? (Challenge Question! Hint, you only have a $50, exactly, with you a. Cost Equation C(m) for m miles is as follows: [B]C(m) = 1.57m + 5 [/B] b. Slope of the equation is the coefficient for m, which is [B]1.57 [/B] c. Total cost of the ride for m = 12 miles is: C(12) = 1.57(12) + 5 C(12) = 18.84 + 5 C(12) = [B]23.84 [/B] d. If you give a 7.50 tip, we subtract the tip from the $50 to start with a reduced amount: 50 - 7.50 = 42.50 So C(m) = 42.50 1.57m + 5 = 42.50 To solve this equation for m, we [URL=' it in our search engine[/URL] and we get: m = 23.89 Since we deal in full miles, we round our answer down to m = [B]23[/B]

If you throw a die for two times, what is the probability that you will get a one on the first throw or a one on the second throw (or both)? [LIST] [*]P(1) on first roll and P(anything on second roll) = 1/6 * 1 = 1/6 [*]P(anything on first roll) and P(1) on second roll = 1 * 1/6 = 1/6 [*]Add those together: 1/6 + 1/6 = 2/6 = [B]1/3[/B] [/LIST]

If you toss a fair coin 6 times, what is the probability of getting all tails? We [URL=' in our search engine [I]TTTTTT [/I]and we get[/URL]: P(TTTTTT) = [B]1/64 or 0.015625[/B]

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. The researcher posed a null hypothesis that the average weight for boys in that high school should be 100 lbs. What is the [B][U]absolute value[/U][/B] of calculated t that we use for testing the null hypothesis? Mean is 109.4 and Standard Deviation = 20.79182532 using our [URL=' calculator[/URL] Now use those values and calculate the t-value Abs(t value) = (100 - 109.4)/ 20.79182532/sqrt(5) Abs(tvalue) = [B]1.010928029[/B]

In 1910, the population of math valley was 15,000. If the population is increasing at an annual rate of 2.4%, what was the population in 1965? 1965 - 1910 = 55 years of growth. P(1965) = 15,000 * (1.024)^55 P(1965) = 15,000 * 3.68551018049 P(1965) = 55282.652707 ~ [B]55,283[/B]

In 20 years charles will be 3 times as old as he is now. How old is he now? Let Charles's age be a today. We're given: a + 20 = 3a [URL=' we type this equation into our search engine[/URL], we get: [B]a = 10 [/B] Let's check our work in our given equation: 10 + 20 ? 3(10) 30 = 30 <-- Checks out!

In 2000 a company increased its workforce by 50%. In 2001 it decreased its workforce by 50%. How does the size of its workforce at the end of 2001 compare with the size of the workforce at the beginning of 2000? Let w be the size of the workforce before any changes. We have: [LIST] [*]w(2000) = w(1999) * 1.5 [I](50% increase is the same as multiplying by 1.5)[/I] [*]w(2001) = w(2000)/1.5 [I](50% decrease is the same as dividing by 1.5)[/I] [/LIST] Substitute the first equation back into the second equation w(2001) = w(1999) * 1.5/1.5 Cancel the 1.5 on top and bottom w(2001) = w(1999) This means the workforce had [B]zero net change[/B] from the beginning of 2000 to the end of 2001.

In 2010 a algebra book cost $125. In 2015 the book cost $205. Whats the linear function since 2010? In 5 years, the book appreciated 205 - 125 = 80 in value. 80/5 = 16. So each year, the book increases 16 in value. Set up the cost function: [B]C(y) = 16y where y is the number of years since 2010[/B]

In 2010, the population of Greenbow, AL was 1,100 people. The population has risen at at rate of 4% each year since. Let x = the number of years since 2010 and y = the population of Greenbow. What will the population of Greenbow be in 2022? P(x) = 1,100(1.04)^x x = 2022 - 2010 x = 12 years We want P(12): P(12) = 1,100(1.04)^12 P(12) = 1,100(1.60103221857) P(12) = [B]1,761.14 ~ 1,761[/B]

In 2016 the geese population was at 750. the geese population is expected to grow at a rate of 12% each year. What is the geese population in 2022? 12% is also 0.12. We have the population growth function: P(t) = 750(1.12)^t 2022 - 2016 is 6 years of growth. We want P(6). P(6) = 750(1.12)^6 P(6) = 750(1.9738) [B]P(6) = 1,480.36 ~ 1,480[/B]

In 2016, National Textile installed a new textile machine in one of its factories at a cost of $300,000. The machine is depreciated linearly over 10 years with a scrap value of $10,000. (a) Find an expression for the textile machines book value in the t?th year of use (0 ? t ? 10) We have a straight line depreciation. Book Value is shown on the [URL=' line depreciation calculator[/URL].

in 6th grade, veronica reads 45 books. in 7th grade she reads 63 books. what is the percent change? Percent Change = 100% * (New Value - Old Value)/Old Value Percent Change = 100% * (63 - 45)/45 Percent Change = 100% * 18/45 Percent Change = 100% * 0.4 Percent Change = [B]40%[/B] [B] There is a percentage increase[/B]

In 8 years kelly's age will be twice what it is now. How old is kelly? Let Kelly's age be a. In 8 years means we add 8 to a: a + 8 Twice means we multiply a by 2: 2a The phrase [I]will be[/I] means equal to, so we set a + 8 equal to 2a a + 8 = 2a To solve this equation, we [URL=' it in our math engine[/URL] and we get: a = [B]8 [/B] [U]Evaluate a = 8 and check our work[/U] 8 + 8 ? 2(8) 16 = 16 [MEDIA=youtube]y4jaQpkaJEw[/MEDIA]

In a booklet there are 25 tickets. Flame needs 75 tickets . How many booklets he need 25 tickets per booklet * b = 75 Booklets needed (b) = 75 / 25 Booklets needed (b) = [B]3[/B]

In a certain lot, there are 16 white, 7 red, 8 blue, and 9 black cars. You randomly pick a set of keys to one of the cars. What is the probability of choosing a set of keys to a blue car? [U]Our total cars are:[/U] Total Cars = White Cars + Red Cars + Blue Cars = Black Cars Total Cars = 16 + 7 + 8 + 9 Total Cars = 40 P(Blue) = Blue Cars / Total Cars P(Blue) = 8/40 Using our [URL=' simplify calculator[/URL], we get: P(Blue) = [B]1/5[/B]

In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there in the class? We start by declaring variables for boys and girls: [LIST] [*]Let b be the number of boys [*]Let g be the number of girls [/LIST] We're given two equations: [LIST=1] [*]b = g + 5 [*]b + g = 13 [/LIST] Substitute equation (1) for b into equation (2): g + 5 + g = 13 Grouping like terms, we get: 2g + 5 = 13 Subtract 5 from each side: 2g + 5 - 5 = 13 - 5 Cancel the 5's on the left side and we get: 2g = 8 Divide each side of the equation by 2 to isolate g: 2g/2 = 8/2 Cancel the 2's on the left side and we get: g = 4 Substitute g = 4 into equation (1) to solve for b: b = 4 + 5 b = [B]9[/B]

In a family of 4 children, what is the probability that all four will be girls? P(G) = 1/2 or 0.5 Since each child is independent, we have: 1/2 * 1/2 * 1/2 * 1/2 or (1/2)^4 [B]1/16 or in decimal form, 0.0625[/B]

In a hurricane the wind pressure varies directly as the square of the wind velocity. If a wind pressure is a measure of a hurricane's destruction capacity, what happens to this destructive power when the wind speed doubles? Let P = pressure and v = velocity (wind speed) We are given p = v^2 Double velocity, so we have a new pressure P2: P2 = (2v)^2 P2 = 4v^2 Compare the 2: p = v^2 p = 4v^2 Doubling the wind speed [B]quadruples, or 4 times[/B] the pressure.

In a paper bag, 7 of the 15 marbles are yellow. In a cloth bag, 2 of the 15 marbles are yellow. If Tim randomly draws one marble from each bag, what is the probability that they are both yellow? Bag 1 probability of drawing yellow is 7/15 Bag 2 probability of drawing yellow is 2/15 Since each event is independent, we multiply each draw to get our final probability: P(yellow Bag 1)(yellow Bag 2) = P(Yellow Bag 1) * P(Yellow Bag 2) P(yellow Bag 1)(yellow Bag 2) = 7/15 * 2/15 P(yellow Bag 1)(yellow Bag 2) = [B]14/225[/B] [URL=' we cannot simplify this fraction anymore[/URL], our answer is [B]14/225[/B]

In a presidential election ohio had 20 electoral votes. This is 14 less than Texas had. How many electoral votes did Texas have? Let 0 = Ohio votes and t = Texas votes. We have: [LIST=1] [*]o = 20 [*]0 = t - 14 [/LIST] [U]Substitute (1) into (2)[/U] 20 = t - 14 [U]Add 14 to each side[/U] [B]t = 34[/B]

In a sample of 80 beetles, 50 beetles had 4 spots each, and the rest had 6 spots each. What was the average number of spots per beetle? Show your work below. Average spots per beetle = Total spots for all beetles / Total beetles Average spots per beetle = (50(4) + 6(80 - 50))/80 Average spots per beetle =(200 + 6(30))/80 Average spots per beetle = (200 + 180)/80 Average spots per beetle = (380)/80 Average spots per beetle = [B]4.75 spots[/B]

In a shipment of 330 animals, 125 were hogs, 68 were sheep, and the rest were cattle. Find the number of cattle in the shipment. To find the rest (cattle), we subtract off the hogs and sheep from the total. Cattle = Total Animals - Hogs - Sheep Cattle = 330 - 125 - 68 [B]Cattle = 137[/B]

In a survey of 420 people, 230 use samsung mobile, 180 use iphone, 90 use both ,find the number of people who don't use either of them People who don't use both is: 420 - (230 + 180 - 90) 420 - (320) [B]100[/B]

In an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the two grades was 180. Let the high grade be h and the low grade be l. We're given: [LIST=1] [*]h = l + 50 [*]h + l = 180 [/LIST] Substitute equation (1) into equation (2) for h l + 50 + l = 180 To solve this equation, [URL=' type it in our search engine[/URL] and we get: l = [B]65 [/B] Now, we take l = 65 and substitute it into equation (1) to solve for h: h = 65 + 50 h = [B]115[/B]

In base 10 the number 25.12 actually means 20 + 5 + 1/10 + 2/100. What does the base 7 number 25.12 mean? 2 groups of 7 5 groups of 1 1 group of 1/7 2 groups of 1/49 (1/7)^2 14 + 5 + 1/7 + 2/49

In base 10, the number .1111... approaches 1/9. What does .111111 base 2 approach in base 10? Base 2 .11111 means: (1/2)^1 + (1/2)^2 + + (1/2)^3 + (1/2)^4 1/2 + 1/4 + 1/8 + 1/16 [B]This approaches 1[/B]

In rolling a die, the event E is getting a number greater than or equal to 3. What is the complement of the event? The complement E' is everything but the event. So we have: E = P(n >= 3) E' = [B]P(n < 3)[/B]

In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game? In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game? Let w be the winning team's points, and l be the losing team's points. We have two equations: [LIST=1] [*]w + l = 41 [*]w - l = 27 [/LIST] Add the two equations: 2w = 68 Divide each side by 2 [B]w = 34[/B] Substitute this into (1) 34 + l = 41 Subtract 34 from each side [B]l = 7[/B] Check your work: [LIST=1] [*]34 + 7 = 41 <-- check [*]34 - 7 = 27 <-- check [/LIST] The final score of the game was [B]34 to 7[/B]. You could also use our [URL=' equation solver[/URL].

In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the library at the end of the year. How many books were in the library at the start of the year Let the starting book count be b. We have: [LIST] [*]We start with b books [*]Buying 237 books means we add (+237) [*]Removing 67 books means we subtract (-67) [*]We end up with 5745 books [/LIST] Our change during the year is found by the equation: b + 237 - 67 = 5745 To solve for b, we [URL=' this equation into our search engine[/URL] and we get: b = [B]5575[/B]

In the wild, monkeys eat an average of 28 bananas a day with a standard deviation of 2 bananas. One monkey eats only 21 bananas. What is the z-score for this monkey? Is the number of bananas the monkey eats unusually low? Using [URL=' z-score calculator[/URL], we get: Z < -3.5 P(Z < -3.5) = 0.499767 Also, this [B]is unusually low as it's more than 3 deviations away from the mean[/B]

In the year 1980, Rick was twice as old as Nancy who was twice as old as Michael. In the year 1992 Ric, Nancy, and Michael ages added up to 78 years. How old was Ric in 1980? Age in 1980: [LIST] [*]Let Michael's age be m [*]Nancy's age is 2m [*]Rick's age is 2 * 2m = 4m [/LIST] Age in 1992: [LIST] [*]Michael's age = m + 12 [*]Nancy's age is 2m + 12 [*]Rick's age is 2 * 2m = 4m + 12 [/LIST] Total them up: m + 12 + 2m + 12 + 4m + 12 = 78 Solve for [I]m[/I] in the equation m + 12 + 2m + 12 + 4m + 12 = 78 [SIZE=5][B]Step 1: Group the m terms on the left hand side:[/B][/SIZE] (1 + 2 + 4)m = 7m [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] 12 + 12 + 12 = 36 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 7m + 36 = + 78 [SIZE=5][B]Step 4: Group constants:[/B][/SIZE] We need to group our constants 36 and 78. To do that, we subtract 36 from both sides 7m + 36 - 36 = 78 - 36 [SIZE=5][B]Step 5: Cancel 36 on the left side:[/B][/SIZE] 7m = 42 [SIZE=5][B]Step 6: Divide each side of the equation by 7[/B][/SIZE] 7m/7 = 42/7 m = 6 Rick's age = 6 * 4 = [B]24 [URL=' [/B]

In the year 1989, Luke's age was 3 times Rachel's age and Rachel's age was 3 times Dan's age. If Dan's age was n, how old were Rachel and Luke? Rachel's age = 3 * Dan's age Rachel's age = 3n Luke's age = 3 times Rachel's age Luke's age = 3(3n) Luke's age = [B]9n[/B]

In the year 1999, Hicham El Guerrouj of Morocco set a new world record when he ran a mile in 3 minutes 43.13 seconds. What was his speed in miles per hour? (Round your answer to the nearest hundredth.) 3 minutes = 60 seconds per minute = 180 seconds 180 seconds + 43.13 seconds = 223.13 seconds 223.13 seconds/3600 seconds per hour = 1 mile/n miles Cross multiply: 223.13n = 3600 Using our [URL=' solver[/URL], we get: n = [B]16.13 miles per hour[/B]

In Trina's desk drawer, there are 15 paper clips and 18 rubber bands. In Kirk's office supply tray, there are 13 paper clips and 16 rubber bands. Who has a higher ratio of paper clips to rubber bands? Trina: 15/18 Kirk: 13/16 We want common denominators to compare, so we get a greatest common factor (GCF) for 16 and 18. [URL=' this through our search engine[/URL], we get GCF(16, 18) = 144 For Trina, 144/18 = 8 For Kirk, 144/16 = 9 We multiply Trina's fraction, top and bottom by 8: 15 * 8 / 18 * 8 120/144 We multiply Trina's fraction, top and bottom by 8: 13 * 8 / 16 * 8 104/144 [B]Trina[/B] has more in her numerator, so her ratio of paper clips to rubber bands is greater.

In which quadrant is the point (2,negative 6) located? We have the point (2, -6). It lies in Quadrant IV. to get this, [URL=' in (2, -6) to the search engine[/URL], and click "Quadrant".

Ina has $40 in her bank account and saves $8 a week. Ree has $200 in her bank account and spends $12 a week. Write an equation to represent each girl. Let w equal the number of weeks, and f(w) be the amount of money in the account after w weeks: [LIST] [*]Ina: [B]f(w) = 40 + 8w[/B] [LIST] [*]We add because Ina saves money, so her account grows [/LIST] [*]Ree: [B]f(w) = 200 - 12w[/B] [LIST] [*]We subtract because Ree saves [/LIST] [/LIST]

Free Inclusive Number Word Problems Calculator - Given an integer A and an integer B, this calculates the following inclusive word problem questions: 1) The Average of all numbers inclusive from A to B 2) The Count of all numbers inclusive from A to B 3) The Sum of all numbers inclusive from A to B

Index form of (5^3)^6 Index form is written as a number raised to a power. Let's simplify by multiply the exponents. Since 6*3 = 18, We have: [B]5^18[/B]

index form of sqrt(x) sqrt(x) = [B]x^1/2[/B]

Free Integers Between Calculator - This calculator determines all integers between two numbers (Decimals)

Free Interpolation Calculator - Given a set of data, this interpolates using the following methods: * Linear Interpolation * Nearest Neighbor (Piecewise Constant) * Polynomial Interpolation

Free Interval Counting Calculator - Evaluates a set of interval counting statements in the form a(b)c.

Free Interval Partition Calculator - Given a partitioned interval, this evaluates the norm (mesh) by calculating each subinterval

Free Inventory Method Calculator - Takes accounting entries using the FIFO (first in first out) and LIFO (last in first out) inventory methods.

Is (1, 3) a solution to the equation y = 3x? Plug in x = 1 into y = 3x: y = 3(1) y = 3 The answer is [B]yes[/B], (1, 3) is a solution to y = 3x

Is (3,10) a solution to the equation y=4x Plug in the numbers to check: 10 ? 4(3) 10 <> 12 No, this is [B]not a solution[/B]

Is (9, 6) a solution to the equation y = x - 3? The ordered pair (x, y) = (9, 6) Plug in x = 9 into y = x - 3: y = 9 - 3 y = 6 [B]Yes, (9, 6) is a solution to the equation y = x - 3[/B]

Is 30 a solution to 2x + 5 = 3x - 25 Let's test x = 30 into our equation: 2(30) + 5 ? 3(30) - 25 60 + 5 ? 90 - 25 65 = 65 [B]Yes, x = 30 is a solution[/B]. If you wanted to solve for x with simplification, you can [URL=' it in our search engine[/URL] and get: x = 30

If we factor your expression, we get: y > x(10% + 1) y> 1.1x Since 10% is 0.1 I read it as y > 110% of x

Is the point (4,7) a solution of the equation y equals 15x minus 8? Plug in x = 4: 15(4) - 8 60 - 8 52 Since 52 <> 4, (4,7) is [U][B]not[/B][/U] a solution of the equation y equals 15x minus 8

Isabel is making face mask. She spends $50 on supplies and plans on selling them for $4 per mask. How many mask does have to make in order to make a profit equal to $90? [U]Set up the cost function C(m) where m is the number of masks:[/U] C(m) = supply cost C(m) = 50 [U]Set up the cost function R(m) where m is the number of masks:[/U] R(m) = Sale Price * m R(m) = 4m [U]Set up the profit function P(m) where m is the number of masks:[/U] P(m) = R(m) - C(m) P(m) = 4m - 50 The problems asks for profit of 90, so we set P(m) = 90: 4m - 50 = 90 To solve this equation for m, we [URL=' it in our search engine[/URL] and we get: m = [B]35[/B]

[SIZE=4]Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only 5 times as old as William? [U]Express Ishaan and William's age since today where y is the number of years since today, we have:[/U] i = 72+y w = 4+y [U]We want the time for Ishaan age will be 5 times William's age:[/U] i = 5w 72 + y = 5(4 + y) We [URL=' this equation into our search engine [/URL]and get: y = [B]13[/B] [/SIZE]

It costs $2.50 to rent bowling shoes. Each game costs $2.25. You have $9.25. How many games can you bowl. Writing an equation and give your answer. Let the number of games be g. we have the function C(g): C(g) = cost per game * g + bowling shoe rental C(g) = 2.25g + 2.50 The problem asks for g when C(g) = 9.25 2.25g + 2.50 = 9.25 To solve this equation, we[URL=' type it in our search engine[/URL] and we get: g = [B]3[/B]

It costs $4.25 per game at the bowling alley plus $1.90 to rent shoes. if Wayne has $20, how many games can he Bowl? Let g be the number of games. The cost for Wayne is: C(g) = Cost per game * number of games + shoe rental 4.25g + 1.90 = C(g) We're given C(g) = 20, so we have: 4.25g + 1.90 = 20 Using our [URL=' solver[/URL] for g, we get: g = 4.25 We need whole games, we we round down to [B]4 games[/B]

it costs $75.00 for a service call from shearin heating and air conditioning company. the charge for labor is $60.00 . how many full hours can they work on my air conditioning unit and still stay within my budget of $300.00 for repairs and service? Our Cost Function is C(h), where h is the number of labor hours. We have: C(h) = Variable Cost * Hours + Fixed Cost C(h) = 60h + 75 Set C(h) = $300 60h + 75 = 300 [URL=' this problem in the search engine[/URL], we get [B]h = 3.75[/B].

It costs a $20 flat fee to rent a lawn mower, plus $5 a day starting with the first day. Let x represent the number of days rented, so y represents the charge to the user (in dollars) Set up our function: [B]y = 20 + 5x[/B]

It is recommended that a ladder be placed 2 feet away from the Wall for every 5 feet of height. How far from the Wall should a 20 foot ladder be placed? Set up a proportion: 2ft away from the wall / 5ft = (x)ft away from the wall / 20ft [URL=' this proportion through our calculator by typing[/URL]: 2/5=x/20 x = [B]8 ft[/B]

It takes 60 minutes for 7 people to paint 5 walls. How many minutes does it take 10 people to paint 10 walls? Rate * Time = Output Let "Rate" (r) be the rate at which [B]one person[/B] works. So we have: 7r * 60 = 5 Multiply through and simplify: 420r = 5 Divide each side by 5 to isolate r: r = 1/84 So now we want to find out how many minutes it takes 10 people to paint 10 walls using this rate: 10rt = 10 With r = 1/84, we have: 10t/84 = 10 Cross multiply: 10t = 840 To solve for t, we t[URL=' this equation into our search engine[/URL] and we get: t = [B]84 minutes[/B]

j - m/4 = 4k for m Multiply each side by 4: 4j - 4m/4 = 4(4k) Simplify: 4j - m = 16k Add m to each side: 4j - m + m = 16k + m The m's cancel on the left side, so we have: 4j = 16k + m Subtract 16k from each side: 4j - 16k = 16k - 16k + m The 16k cancels on the right side, so we're left with: [B]m = 4j - 16k or 4(j - 4k)[/B]

Jack bought 7 tickets for a movie. He paid $7 for each adult ticket and $4 for each child ticket. Jack spent $40 for the tickets Let a = Number of adult tickets and c be the number of child tickets. [LIST=1] [*]7a + 4c = 40 [*]a + c = 7 [*]Rearrange (2): a = 7 - c [/LIST] Now substitute a in (3) into (1): 7(7 - c) + 4c = 40 49 - 7c + 4c = 40 49 - 3c = 40 Add 3c to each side and subtract 40: 3c = 9 Divide each side by 3: [B]c = 3 [/B] Substitute c = 3 into Equation (2) a + 3 = 7 Subtract 3 from each side: [B]a = 4[/B]

Jack bought a car for $17,500. The car loses $750 in value each year. Which equation represents the situation? Let y be the number of years since Jack bought the car. We have a Book value B(y): [B]B(y) = 17500 - 750y[/B]

Jack is making snack bags. He has 18 baby carrots and 42 pretzels. He wants to divide them equally among the bags. What is the greatest number of snack bags he can make? Find the [URL=' Common Factor[/URL] of (18, 42) = 6 6 bags for 18 carrots = 3 carrots per bag 6 bags for 42 pretzels = 7 pretzels per bag [B]6 bags is the answer[/B]

Jack scored a mean of 15 points per game in his first 3 basketball games. In his 4th grade, he scored 27 points. What was Jack's mean score for the four games? The mean is the average: Mean = (15 + 15 + 15 + 27)/4 Mean = 72/4 [B]Mean = 18[/B]

Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episode airs, Jake receives a bunch of fan mail. He splits all the letters into 3 equal stacks to open with his mom and his sister. Each stack contains 21 letters. Which equation can you use to find the number of letters n Jake receives? The number of letters n is represented by number of stacks (s) times letter per stack (l). We're given s = 3 and l = 21, so we have: n = 21(3) n = [B]63[/B]

Jake earns 25% commission selling ice cream. How much does he earn for each days sale? [LIST] [*]a) Friday $100 [*]b) Saturday $180 [/LIST] Commission = Sales * Commission Percent [U]Calculate part a:[/U] Commission = 100 * 25% Commission = [B]$25[/B] [U]Calculate part b:[/U] Commission = 180 * 25% Commission = [B]$45[/B]

James has a weekly allowance of 5 plus 1.50 for each chore c he does We build the allowance function A(c) where c is each chore A(c) = cost per chore * c + Weekly Allowance Plugging in our numbers, we get: [B]A(c) = 1.50c + 5[/B]

James is four time as old as peter if their combined age is 30 how old is James. Let j be Jame's age. Let p be Peter's age. We're given: [LIST=1] [*]j = 4p [*]j + p = 30 [/LIST] Substitute (1) into (2) 4p + p = 30 Combine like terms: 5p = 30 [URL=' 5p = 30 into our search engine[/URL], and we get p = 6. Plug p = 6 into equation (1) to get James's age, we get: j = 4(6) j = [B]24[/B]

Janice says that the sum of the measures of the interior angles of an octagon is 900. Is Janice correct? Why or why not? She's [B]incorrect. [/B] The interior angle sum for a polygon is found with this formula: Interior Angle Sum = (sides - 2) x 180 Since an octagon has 8 sides, we have: Interior Angle Sum = (8 - 2) x 180 Interior Angle Sum = 6 x 180 Interior Angle sum = 1080

Jason has an equal number of nickels and dimes. The total value of his nickels and dimes is $2.25. How many nickels does Jason have? Let the number of nickels be n Let the number of dimes be d We're given two equations: [LIST=1] [*]d = n [*]0.05n + 0.1d = 2.25 [/LIST] Substitute equation (1) for d into equation (2): 0.05n + 0.1n = 2.25 Solve for [I]n[/I] in the equation 0.05n + 0.1n = 2.25 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (0.05 + 0.1)n = 0.15n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 0.15n = + 2.25 [SIZE=5][B]Step 3: Divide each side of the equation by 0.15[/B][/SIZE] 0.15n/0.15 = 2.25/0.15 n = [B]15[/B] [URL='

[SIZE=6]Jason is 9 miles ahead of Joe running at 5.5 miles per hour and Joe is running at the speed of 7 miles per hour. How long does it take Joe to catch Jason? A. 3 hours B. 4 hours C. 6 hours D. 8 hours Distance formula is d = rt Jason's formula (Add 9 since he's ahead 9 miles): d = 5.5t + 9 Joe's formula: d = 7t Set both distance formulas equal to each other: 5.5t + 9 = 7t Subtract 5.5t from each side: 5.5t - 5.5t + 9 = 7t - 5.5t 1.5t = 9 Divide each side by 1.5: 1.5t/1.5 = 9/1.5 t = [B]6 hours[/B] [U]Check our work with t = 6[/U] Joe = 7(6) = 42 Jason = 5.5(6) + 9= 33 + 9 = 42 [MEDIA=youtube]qae3WCq9wzM[/MEDIA] [/SIZE]

Jay earns S amount per day for working in a company. His total expenses per day is equal to the amount E. Write an expression to show how much he earned per day in a month. Suppose he is working for 20 days per month. [LIST=1] [*]Each day, Jay earns a profit of S - E. [*]For one month (30 days), he earns 30(S - E) [*]For 20 working days in a month, he earns 20(S - E) [/LIST]

Jay purchased tickets for a concert. To place the order, a handling charge of $7 per ticket was charged. A sales tax of 4% was also charged on the ticket price and the handling charges. If the total charge for four tickets was $407.68, what was the ticket price? Round to the nearest dollar. with a ticket price of t, we have the total cost written as: 1.04 * (7*4 + 4t)= 407.68 Divide each side by 1.04 1.04 * (7*4 + 4t)/1.04= 407.68/1.04 Cancel the 1.04 on the left side and we get: 7*4 + 4t = 392 28 + 4t = 392 To solve this equation for t, we [URL=' it in our math engine[/URL] and we get: t = [B]91[/B]

Jazmin is a hairdresser who rents a station in a salon for daily fee. The amount of money (m) Jazmin makes from any number of haircuts (n) a day is described by the linear function m = 45n - 30 A) A haircut costs $30, and the station rent is $45 B) A haircut costs $45, and the station rent is $30. C) Jazmin must do 30 haircuts to pay the $45 rental fee. D) Jazmin deducts $30 from each $45 haircut for the station rent. [B]Answer B, since rent is only due once. Profit is Revenue - Cost[/B]

Jeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An employee in the Amazon distribution center earns about $13 an hour. The estimated lifespan of the employee is 71 years. If the employee worked 24 hours a day, every day of the year from the moment of his birth, how many lifespans would it take for him to earn wages equivalent to Jeff Bezos' net worth? Round the answer to the nearest whole number. Calculate earnings per lifespan: Earnings per lifespan = lifespan in years * Annual Earnings Earnings per lifespan = 71 * 13 * 24 * 365 <-- (24 hours per day * 365 days per year) Earnings per lifespan = 8,085,480 Calculate the number of lifespans needed to match Jeff Bezos earnings: Number of lifespans = Jeff Bezos Net Worth / Earnings Per Lifespan Number of lifespans = 143,100,000,000 / 8,085,480 Number of lifespans = [B]17,698.39 ~ 17,699[/B]

Jelaskan secara tepat, memperagakan balok garis bilangan untuk menjelaskan bentuk operasi (-6)-(-8) Tolak negatif adalah positif. Oleh itu, kami mempunyai: -6 + 8 = [B]2 Pada garis nombor, kita mulai pada -6 dan beralih ke kanan 8 unit menjadi 2[/B]

Jennifer has 26 less than triple the savings of Matthew. Matthew has saved 81. How much has Jennifer saved? Let Jennifer's savings be j. We're given: j = 3(81) - 26 j = 243 - 26 j = [B]217[/B]

Jennifer is playing cards with her bestie when she draws a card from a pack of 25 cards numbered from 1 to 25. What is the probability of drawing a number that is square? The squares from 1 - 25 less than or equal to 25 are as follows: [LIST=1] [*]1^2 = 1 [*]2^2 = 4 [*]3^2 = 9 [*]4^2 = 16 [*]5^2 = 25 [/LIST] So the following 5 cards are squares: {1, 4, 9, 16, 25} Therefore, our probability of drawing a square is: P(square) = Number of Squares / Number of Cards P(square) = 5/25 This fraction can be simplified. So [URL=' type in 5/25 into our search engine, choose simplify[/URL], and we get: P(square) = [B]1/5[/B]

Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age Let j be Jennifer's age Let p be Peter's age We're given two equations: [LIST=1] [*]j = 2p [*]j - p = 15 [/LIST] Substitute equation (1) into equation (2) for j 2p - p = 15 To solve for p, we [URL=' this equation into our calculation engine[/URL] and we get: p = [B]15[/B]

Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how many weeks will Jenny and Kelsey have the same amount of money? Jenny: Let w be the number of weeks. Spending means we subtract, so we set up a balance equation B(w): B(w) = 1200 - 40w Kelsey: Let w be the number of weeks. Saving means we add, so we set up a balance equation B(w): B(w) = 120 + 50w When they have the same amount of money, we set the balance equations equal to each other: 1200 - 40w = 120 + 50w To solve for w, we [URL=' this equation into our search engine[/URL] and we get: w = [B]12[/B]

Jenny makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours. Since Jenny makes 9 dollars for each hour of work, then her total pay (p) is her hourly rate times the number of hours worked: [B]p = 9h[/B]

Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined distance thrown by the 3 friends is 124 metres, how far did Angus throw the javelin? Assumptions and givens: [LIST] [*]Let a be the distance Angus threw the javelin [*]Let c be the distance Cameron threw the javelin [*]Let j be the distance Jenny threw the javelin [/LIST] We're given 3 equations: [LIST=1] [*]j = a + 4 [*]j = c - 5 [*]a + c + j = 124 [/LIST] Since j is the common variable in all 3 equations, let's rearrange equation (1) and equation (2) in terms of j as the dependent variable: [LIST=1] [*]a = j - 4 [*]c = j + 5 [*]a + c + j = 124 [/LIST] Now substitute equation (1) and equation (2) into equation (3) for a and c: j - 4 + j + 5 + j = 124 To solve this equation for j, we [URL=' it in our math engine[/URL] and we get: j = 41 The question asks how far Angus (a) threw the javelin. Since we have Jenny's distance j = 41 and equation (1) has j and a together, let's substitute j = 41 into equation (1): a = 41 - 4 a = [B]37 meters[/B]

Jenny went shoe shopping. Now she has 5 more pairs than her brother. Together they have 25 pairs. How many pairs does Jenny have and how many pairs does her brother have? [U]Let j be the number of shoes Jenny has and b be the number of s hoes her brother has. Set up 2 equations:[/U] (1) b + j = 25 (2) j = b + 5 [U]Substitute (2) into (1)[/U] b + (b + 5) = 25 [U]Group the b terms[/U] 2b + 5 = 25 [U]Subtract 5 from each side[/U] 2b = 20 [U]Divide each side by b[/U] [B]b = 10 [/B] [U]Substitute b = 10 into (2)[/U] j = 10 + 5 [B]j = 15[/B]

Jessica has 16 pairs of shoes. She buys 2 additional pair of shoes every month. What is the slope in this situation? Set up a graph where months is on the x-axis and number of shoes Jessica owns is on the y-axis. [LIST=1] [*]Month 1 = (1, 18) [*]Month 2 = (2, 20) [*]Month 3 = (3, 22) [*]Month 4 = (4, 24) [/LIST] You can see for every 1 unit move in x, we get a 2 unit move in y. Pick any of these 2 points, and [URL=' our slope calculator[/URL] to get: Slope = [B]2[/B]

Jessica tutors chemistry. For each hour that she tutors, she earns 30 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H . Then use this equation to find Jessicas earnings after tutoring for 19 hours. Set up a function of h hours for tutoring: [B]E(h) = 30h[/B] We need to find E(19) E(19) = 30(19) E(19) = [B]570[/B]

Jim has $440 in his savings account and adds $12 per week to the account. At the same time, Rhonda has $260 in her savings account and adds $18 per week to the account. How long will it take Rhonda to have the same amount in her account as Jim? [U]Set up Jim's savings function S(w) where w is the number of weeks of savings:[/U] S(w) = Savings per week * w + Initial Savings S(w) = 12w + 440 [U]Set up Rhonda's savings function S(w) where w is the number of weeks of savings:[/U] S(w) = Savings per week * w + Initial Savings S(w) = 18w + 260 The problems asks for w where both savings functions equal each other: 12w + 440 = 18w + 260 To solve for w, we [URL=' this equation into our math engine[/URL] and we get: w = [B]30[/B]

Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82, how old is the eldest of them Let j be Jim's age, a be Alex's age, and u be June's age. We have 3 given equations: [LIST=1] [*]j + a + u = 82 [*]j = u + 9 [*]a = u - 8 [/LIST] Substitute (2) and (3) into (1) (u + 9) + (u - 8) + u = 82 Combine Like Terms: 3u + 1 = 82 [URL=' this equation into the search engine[/URL], and we get u = 27. The eldest (oldest) of the 3 is Jim. So we have from equation (2) j = u + 9 j = 27 + 9 [B]j = 36[/B]

Jim was thinking of a number. Jim adds 20 to it, then doubles it and gets an answer of 99.2. What was the original number? Start with x. Add 20 to it x + 20 Double it 2(x + 20) Set this equal to 99.2 2(x + 20) = 99.2 Divide each side by 2: x + 20 = 49.6 Subtract 20 from each side: x = [B]29.6[/B]

Jim works for his dad and earns $400 every week plus $22 for every chair (c) he sells. Write an equation that can be used to determine jims weekly salary (S) given the number of chairs (c) he sells. [B]S(c) = 400 + 22c[/B]

Jina's test score average decreased by 10 points this semester. Write a signed number to represent this change in average. Let A be the original average. The new average is: A + (-10)

Jody is buying a scrapbook and sheets of designer paper. She has $40 and needs at least $18.25 to buy the scrapbook. Each sheet of paper costs $0.34. How many sheets of paper can she buy? Set up a cost equation for the number of pieces of paper (p): 0.34p + 18.25 <= 40 <-- we have an inequality since we can't go over 40 [URL=' this inequality into our search engine[/URL] and we get: p <= 63.97 We round down, so we get p = [B]63[/B].

Joe earns $9 per hour. He worked x hours on both Wednesday and Friday, and 8 hours on both Tuesday and Saturday. Write an expression to represent how much joe earned. Earnings = Hourly Rate * hours worked, so we have: [LIST] [*]Wednesday: 9x [*]Friday: 9x [*]Tuesday: 9(8) = 72 [*]Saturday: 9(8) = 72 [/LIST] Joe's total earnings come from adding up all 4 days: 9x + 9x + 72 + 72 Combine like terms: (9 + 9)x + (72 + 72) [B]18x + 144[/B]

Joe opens a bank account that starts with $20 and deposits $10 each week. Bria has a different account that starts with $1000 but withdraws $15 each week. When will Joe and Bria have the same amount of money? Let w be the number of weeks. Deposits mean we add money and withdrawals mean we subtract money. [U]Joe's Balance function B(w) where w is the number of weeks:[/U] 20 + 10w [U]Bria's Balance function B(w) where w is the number of weeks:[/U] 1000 - 15w [U]The problem asks for when both balances will be the same. So we set them equal to each other and solve for w:[/U] 20 + 10w = 1000 - 15w To solve for w, we [URL=' this equation into our search engine[/URL] and we get: w = 39.2 We round up to full week and get: w = [B]40[/B]

Joey and Romnick play in the same soccer team. Last Saturday, Romnick scored 3 more goals than Joey,but together they scored less than 9 goals. What are the possible number of goal Romnick scored? Let j be Joey's goals Let r by Romnick's goals We're given 1 equation and 1 inequality: [LIST=1] [*]r = j + 3 [*]r + j < 9 [/LIST] Rearranging equation 1 for j, we have: [LIST=1] [*]j = r - 3 [*]r + j < 9 [/LIST] Substitute equation (1) into inequality (2) for j: r + r - 3 < 9 2r - 3 < 9 [URL=' this inequality into our math engine[/URL], we get: [B]r < 6[/B]

John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and Jane, then John has how many more blue marbles than Jane? John's red ratio = 18/30 Using a [URL=' for (18, 30)[/URL], we get 6. Divide top and bottom of 18/30 by 6, we get 3/5 John's blue ratio is 12/30 Using a [URL=' of (12, 30)[/URL], we get 6. Divide top and bottom of 12/30 by 6, we get 2/5 Use these same ratios for Jane, we get: Red: 3(20)/5 = 12 Blue: 20 - 12 = 8 Now the problem asks how many more blue marbles John has then Jane. We have 12 - 8 = [B]4[/B].

John is paid a retainer of $550 a week as well as a 2% commission on sales made. Find his income for the week if in one week he sells cars worth of $80000 Set up the income function C(s) where s is the number of sales for a week. Since 2% can be written as 0.02, we have: I(s) = Retainer + 2% of sales I(s) = 550 + 0.02s The problem asks for a I(s) where s = 80,000: I(s) = 550 + 0.02(80000) I(s) = 550 + 1600 I(s) = [B]2150[/B]

John read the first 114 pages of a novel, which was 3 pages less than 1/3 Set up the equation for the number of pages (p) in the novel 1/3p - 3 = 114 Add 3 to each side 1/3p = 117 Multiply each side by 3 [B]p = 351[/B]

John took 20,000 out of his retirement and reinvested it. He earned 4% for one investment and 5% on the other. How much did he invest in each if the total amount earned was 880? The first principal portion is x. Which means the second principal portion is 20,000 - x. We have: 0.04x + 0.05(20,000 - x) = 880 0.04x + 1,000 - 0.05x = 880 Group like terms: -0.01x + 1000 = 880 Using our [URL=' solver[/URL], we get x = [B]12,000[/B]. Which means the other fund has 20,000 - 12,000 = [B]8,000[/B].

Free Joint Variation Equations Calculator - Given a joint variation (jointly proportional) of a variable between two other variables with a predefined set of conditions, this will create the joint variation equation and solve based on conditions. Also called combined variation.

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month? [U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 10% written as a decimal is 0.1. We want decimals to solve equations easier. S(m) = 0.1m + 1500 [U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 15% written as a decimal is 0.15. We want decimals to solve equations easier. S(m) = 0.15m + 1200 [U]The question asks what is m when both S(m)'s equal each other[/U]: The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other 0.1m + 1500 = 0.15m + 1200 We want to isolate m terms on one side of the equation. Subtract 1200 from each side: 0.1m + 1500 - 1200 = 0.15m + 1200 - 1200 Cancel the 1200's on the right side and we get: 0.1m - 300 = 0.15m Next, we subtract 0.1m from each side of the equation to isolate m 0.1m - 0.1m + 300 = 0.15m - 0.1m Cancel the 0.1m terms on the left side and we get: 300 = 0.05m Flip the statement since it's an equal sign to get the variable on the left side: 0.05m = 300 To solve for m, we divide each side of the equation by 0.05: 0.05m/0.05 = 300/0.05 Cancelling the 0.05 on the left side, we get: m = [B]6000[/B]

Josh currently bench presses 150 lbs. He increases that amount by 10% a month for 3 months. About how much can he bench press now? We have 150(1.1)^3. We can also write this as 150(1.1)(1.1)(1.1). The 10% compounds. After 3 months, Josh benches 199.65 lbs, or approximately 200 lbs.

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51 Let JP's age be j. Let Reyna's age be r. We're given two expressions: [LIST=1] [*]w = 2r [*]r + w <= 51. ([I]Does not exceed means less than or equal to)[/I] [/LIST] We substitute (1) into (2) for w to get the inequality: r + 2r <= 51 To solve this inequality, we type it in our search engine and we get: [B]r <= 17[/B]

Juan spent at most $2.50 on apples and oranges. He bought 5 apples at $0.36 each. What is the most he spent on oranges? Let a be spending apples and o be spending on oranges, we have: [LIST=1] [*]a + o <= 2.36 <-- At most means less than or equal to [*]a = 5 * 0.36 = 1.8 [/LIST] Substitute (2) into (1) 1.8 + o <= 2.36 Subtract 1.8 from each side [B]o <= 0.56[/B]

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and .10 cents for additional texts. How many texts did she send out? Let m be the number of messages. We have a cost function of: C(m) = 9 + 0.1(m - 600) We are given C(m) = 18.20 18.20 = 9 + 0.1(m - 600) 18.20 = 9 + 0.1m - 60 Combine like terms: 18.20 = 0.1m - 51 Add 51 to each side 0.1m = 69.20 Divide each side by 0.1 [B]m = 692[/B]

Julio has $150. Each week, he saves an additional $10. Write a function f(x) that models the total amount of money Julio has after x weeks f(x) = Savings per week * number of weeks + starting amount f(x) = [B]10x + 150[/B]

Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. What age is Martina? [U]Assumptions and givens:[/U] [LIST] [*]Let Justin's age be j [*]Let Martina's age be m [*]j > m ([I]since Justin is older than Martina[/I]) [/LIST] We're given the following equations : [LIST=1] [*]j - m = 22 [*]j + m = 54 [/LIST] Since the coefficients of m are opposites, we can take a shortcut using the [I]elimination method[/I] and add equation (1) to equation (2) (j + j) + (m - m) = 22 + 54 2j = 76 To solve for j, we [URL=' this equation into our math engine[/URL] and we get: j = 38 The question asks for Martina's age (m), so we can pick equation (1) or equation (2). Let's use equation (1): 38 - m = 22 To solve this equation for m, we [URL=' it in our math engine[/URL] and we get: m = [B]16[/B]

k add 2 multiply by 6 then subtract 8 k add 2: k + 2 Multiply by 6: 6(k + 2) Then subtract 8: [B]6(k + 2) - 8[/B]

k add d , multiply by e , then subtract f . [LIST] [*]k add d: k + d [*]Multiply by e: e(k + d) [*]Then subtract f: [B]e(k + d) - f[/B] [/LIST]

K varies inversely with square root of m and directly with the cube of n. [LIST] [*]We take a constant c as our constant of proportionality. [*]The word inversely means we divide [*]The word directly means we multiply [/LIST] [B]k = cn^3/sqrt(m)[/B]

Kaitlin is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of Math is Fun she sells. Suppose that x and y are related by the equation 2500+110x=y. What is Kaitlin totalm pay if she doesnt sell any copies of Math is Fun? We want the value of y when x = 0. y = 2500 + 110(o) y = 2500 + 0 [B]y = 2500[/B]

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft squared. What are the dimensions of the kennel? How many feet of fencing did she use? Explain. Area of a square with side length (s) is: A = s^2 Given A = 64, we have: s^2 = 64 [URL='(64%2F1)&pl=Simplify+Radical+Expression']Typing this equation into our math engine[/URL], we get: s = 8 Which means the dimensions of the kennel are [B]8 x 8[/B]. How much fencing she used means perimeter. The perimeter P of a square with side length s is: P = 4s [URL=' s = 8, we have[/URL]: P = 4 * 8 P = [B]32[/B]

Karen earns $20 per hour and already has $400 saved, and wants to save $1200. How many hours until bob gets his $1200 goal? Set up he savings function S(h) where h is the number of hours needed: S(h) = savings per hour * h + current savings amount S(h) = 20h + 400 The question asks for h when S(h) = 1200: 20h + 400 = 1200 To solve for h, we [URL=' this equation into our search engine[/URL] and we get: h = [B]40[/B]

Karmen just got hired to work at Walmart. She spent $15 on her new uniform and she gets paid $8 per hour. Write an equation that represents how much money she profits after working for a certain number of hours. How many hours will she have to work for in order to buy a new snowboard ( which costs $450) Her profit equation P(h) where h is the number of hours worked is: [B]P(h) = 8h - 15[/B] Note: [I]We subtract 15 as the cost of Karmen's uniform. [/I] Next, we want to see how many hours Karmen must work to buy a new snowboard which costs $450. We set the profit equation equal to $450 8h - 15 = 450 [URL=' 8h - 15 = 450 into the search engine[/URL], we get h = 58.13. We round this up to 59 hours.

kate is twice as old as her sister mars. the sum of their ages is 24. find their ages. Let k be Kate's age Let m be Mars's age We're given two equations: [LIST=1] [*]k = 2m. (Because twice means multiply by 2) [*]k + m = 24 [/LIST] Substitute equation (1) for k into equation (2): 2m + m = 24 T o solve for m, we [URL=' this equation into our math engine[/URL]: m = [B]8 [/B] We want to solve for k using m= 8. Substitute this into equation 1 k = 2(8) k = [B]16 [/B] Check our work for equation 1 16 = 2 * 8 16 = 16 Check our work for equation 2 16 + 8 ? 24 24 = 24 [MEDIA=youtube]TJMTRYP-Ct8[/MEDIA]

Kate spent 1 more than Lauren, and together they spent 5. Let k be the amount Kate spent, and l be the amount Lauren spent. We're given: [LIST=1] [*]k = l + 1 [*]k + l = 5 [/LIST] Substitute (1) into (2): (l + 1) + l = 5 Group like terms 2l + 1 = 5 [URL=' this equation into our search engine[/URL], we get: [B]l = 2[/B] Plug this into Equation (1), we get: k = 2 + 1 [B]k = 3 [/B] Kate Spent 3, and Lauren spent 2

Kate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the most She spent on oranges [U]Assumptions and givens:[/U] [LIST] [*]Let a be the total cost of apples [*]Let o be the total cost of oranges [/LIST] The phrase [I]at most[/I] means less than or equal to, so we have: a + o <= 2.50 [U]Find the cost of apples (a)[/U] a = price per apple * quantity of apples a = 0.36 * 5 a = 1.8 Our new inequality with a = 1.8 is: 1.8 + o <= 2.50 [URL=' this inequality into our search engine[/URL], we get: [B]o <= 0.7[/B]

Let k = Katie's age and m = Mara's age. We have 2 equations: (1) k = 2m (2) k + m = 24 Substitute (1) into (2) (2m) + m = 24 Combine like terms: 3m = 24 Divide each side of the equation by 3 to isolate m m = 8 If m = 8, substituting into (1) or (2), we get k = 16. [MEDIA=youtube]Cu7gSgNkQPg[/MEDIA]

keisha is babysitting at 8$ per hour to earn money for a car. So far she has saved $1300. The car that keisha wants to buy costs at least $5440. How many hours does Keisha need to babysit to earn enough to buy the car Set up the Earning function E(h) where h is the number of hours Keisha needs to babysit: E(h) = 8h + 1300 The question asks for h when E(h) is at least 5440. The phrase [I]at least[/I] means an inequality, which is greater than or equal to. So we have: 8h + 1300 >= 5440 To solve this inequality, we [URL=' it in our search engine[/URL] and we get: h >= [B]517.5[/B]

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account. Keith's balance is written as B(w) where w is the number of weeks passed since the beginning of summer. We have: B(w) = 500 - 25w The problem asks for B(w) = 200, so we set 500 - 25w = 200. [URL=' 500 - 25w = 200 into the search engine[/URL], we get [B]w = 12[/B].

Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slacks and paid11.45. Then she brought 5 shirts, 3 pairs of slacks, and 1 sports coat and paid 27.41. Finally, she brought 5 shirts and 1 sports coat and paid 16.94. How much was she charged for each shirt, each pair of slacks, and each sports coat? Let s be the cost of shirts, p be the cost of slacks, and c be the cost of sports coats. We're given: [LIST=1] [*]4s + p = 11.45 [*]5s + 3p + c = 27.41 [*]5s + c = 16.94 [/LIST] Rearrange (1) by subtracting 4s from each side: p = 11.45 - 4s Rearrange (3)by subtracting 5s from each side: c = 16.94 - 5s Take those rearranged equations, and plug them into (2): 5s + 3(11.45 - 4s) + (16.94 - 5s) = 27.41 Multiply through: 5s + 34.35 - 12s + 16.94 - 5s = 27.41 [URL=' like terms using our equation calculator [/URL]and we get: [B]s = 1.99 [/B] <-- Shirt Cost Plug s = 1.99 into modified equation (1): p = 11.45 - 4(1.99) p = 11.45 - 7.96 [B]p = 3.49[/B] <-- Slacks Cost Plug s = 1.99 into modified equation (3): c = 16.94 - 5(1.99) c = 16.94 - 9.95 [B]c = 6.99[/B] <-- Sports Coat cost

Kendra has $5.70 in quarters and nickels. If she has 12 more quarters than nickels, how many of each coin does she have? Let n be the number of nickels and q be the number of quarters. We have: [LIST=1] [*]q = n + 12 [*]0.05n + 0.25q = 5.70 [/LIST] Substitute (1) into (2) 0.05n + 0.25(n + 12) = 5.70 0.05n + 0.25n + 3 = 5.70 Combine like terms: 0.3n + 3 = 5.70 Using our [URL=' calculator[/URL], we get [B]n = 9[/B]. Substituting that back into (1), we get: q = 9 + 12 [B]q = 21[/B]

Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How old are they? Let k be Kendra's age, m be Morgan's age, and l be Lizzie's age. We're given: [LIST=1] [*]k = 0.5m [*]k = l - 3 [*]k + l + m = 39 [/LIST] Rearranging (1) by multiplying each side by 2, we have: m = 2k Rearranging (2) by adding 3 to each side, we have: l = k + 3 Substituting these new values into (3), we have: k + (k + 3) + (2k) = 39 Group like terms: (k + k + 2k) + 3 = 39 4k + 3 = 39 [URL=' this equation into the search engine[/URL], and we get: [B]k = 9 [/B] Substitute this back into (1), we have: m = 2(9) [B]m = 18 [/B] Substitute this back into (2), we have: l = (9) + 3 [B][B]l = 12[/B][/B]

Kerry asked a bank teller to cash 390 check using 20 bills and 50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive? Let t = number of 20 bills and f = number of 50 bills. We have two equations. (1) 20t + 50f = 390 (2) t + f = 15 [U]Rearrange (2) into (3) for t, by subtracting f from each side:[/U] (3) t = 15 - f [U]Now substitute (3) into (1)[/U] 20(15 - f) + 50f = 390 300 - 20f + 50f = 390 [U]Combine f terms[/U] 300 + 30f = 390 [U]Subtract 300 from each side[/U] 30f = 90 [U]Divide each side by 30[/U] [B]f = 3[/B] [U]Substitute f = 3 into (3)[/U] t = 15 - 3 [B]t = 12[/B]

Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The total value of the jar is $7.85. How many of each type? Let d be dimes and q be quarters. Set up two equations from our givens: [LIST=1] [*]d + q = 41 [*]0.1d + 0.25q = 7.85 [/LIST] [U]Rearrange (1) by subtracting q from each side:[/U] (3) d = 41 - q [U]Now, substitute (3) into (2)[/U] 0.1(41 - q) + 0.25q = 7.85 4.1 - 0.1q + 0.25q = 7.85 [U]Combine q terms[/U] 0.15q + 4.1 = 7.85 [U]Using our [URL=' calculator[/URL], we get:[/U] [B]q = 25[/B] [U]Substitute q = 25 into (3)[/U] d = 41 - 25 [B]d = 16[/B]

Kevin borrowed $8000 at a rate of 7.5%, compounded monthly. Assuming he makes no payments, how much will he owe after 10 years? We want to find 8,000(1.075)^10 Using our [URL=' calculator[/URL], we get: [B]$16,488.25[/B]

Kevin is 4 times old as Daniel and is also 6 years older than Daniel. Let k be Kevin's age and d be Daniel's age. We have 2 equations: [LIST=1] [*]k = 4d [*]k = d + 6 [/LIST] Plug (1) into (2): 4d = d + 6 Subtract d from each side: 4d - d = d - d + 6 Cancel the d terms on the right side and simplify: 3d = 6 Divide each side by 3: 3d/3 = 6/3 Cancel the 3 on the left side: d = 2 Plug this back into equation (1): k = 4(2) k = 8 So Daniel is 2 years old and Kevin is 8 years old

Kevin ran 4 miles more than Steve ran. The sum of their distances is 26 miles. How far did Steve run? The domain of the solution is: Let k be Kevin's miles ran Let s be Steve's miles ran We have 2 given equtaions: [LIST=1] [*]k = s + 4 [*]k + s = 26 [/LIST] Substitute (1) into (2) (s + 4) + s = 26 2s + 4 = 26 Plug this into our [URL=' calculator[/URL] and we get s = 11

Kiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. What is their present age? Let k be Kiko's present age Let s be Kiko's sisters age. We're given two equations: [LIST=1] [*]k = 6s [*]k + 6 = 3(s + 6) [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for k: 6s + 6 = 3(s + 6) [URL=' this equation into our math engine[/URL] to solve for s, we get: s = [B]4[/B] To solve for k, we substitute s = 4 into equation (1) above: k = 6 * 4 k = [B]24[/B]

kim and jason just had business cards made. kims printing company charged a one time setup fee of $8 and then $20 per box of cards. jason,meanwhile ordered his online. they cost $8 per box. there was no setup fee, but he had to pay $20 to have his order shipped to his house. by coincidence, kim and jason ended up spending the same amount on their business cards. how many boxes did each buy? how much did each spend? Set up Kim's cost function C(b) where b is the number of boxes: C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee C(b) = 20c + 8 + 0 Set up Jason's cost function C(b) where b is the number of boxes: C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee C(b) = 8c + 0 + 20 Since Kim and Jason spent the same amount, set both cost equations equal to each other: 20c + 8 = 8c + 20 [URL=' this equation into our search engine[/URL] to solve for c, and we get: c = 1 How much did they spend? We pick either Kim's or Jason's cost equation since they spent the same, and plug in c = 1: Kim: C(1) = 20(1) + 8 C(1) = 20 + 8 C(1) = [B]28 [/B] Jason: C(1) = 8(1) + 20 C(1) = 8 + 20 C(1) = [B]28[/B]

Kim earns $30 for babysitting on Friday nights. She makes an average of $1.25 in tips per hour. Write the function of Kim's earnings, and solve for how much she would make after 3 hours. Set up the earnings equation E(h) where h is the number of hours. We have the function: E(h) = 1.25h + 30 The problem asks for E(3): E(3) = 1.25(3) + 30 E(3) = 4.75 + 30 E(3) = [B]$34.75[/B]

Kim, Jenny, and Wendy are basketball players. Each plays a different position (guard, forward, and center) and wears a different number (30, 32, and 35).Kim and number 30 are too small to play center. Number 35 is the center. Neither Kim nor Wendy is the forward. Who plays guard, and what uniform number does she wear? [LIST] [*]Kim does not play center [*]Kim does not play forward [*]Which means [B]Kim is the guard[/B] [*]Since Kim is not number 30, and she cannot be number 35 since Number 35 is the center, the only number left is [B]Number 32[/B] [/LIST] [B]Kim is the guard with number 32[/B]

Kimberly wants to become a member of the desert squad at a big catering company very badly, but she must pass three difficult tests to do so. On the first Terrifying Tiramisu test she scored a 68. On the second the challenging Chocalate-Sprinkled Creme Brulee she scored a 72. If kimberly needs an average of 60 on all three tests to become a member on the squad what is the lowest score she can make on her third and final test This is a missing average problem. Given 2 scores of 68, 72, what should be score number 3 in order to attain an average score of 60? [SIZE=5][B]Setup Average Equation:[/B][/SIZE] Average = (Sum of our 2 numbers + unknown score of [I]x)/[/I]Total Numbers 60 = (68 + 72 + x)/3 [SIZE=5][B]Cross Multiply[/B][/SIZE] 68 + 72 + x = 60 x 3 x + 140 = 180 [SIZE=5][B]Subtract 140 from both sides of the equation to isolate x:[/B][/SIZE] x + 140 - 140 = 180 - 140 x = [B]40[/B]

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Kris wants to fence in her square garden that is 40 feet on each side. If she places posts every 10 feet, how many posts will she need? Perimeter (P) of a square with side s: P = 4s Given s = 40, we have: P = 4(40) P = 160 feet 160 feet / 10 foot spaces = [B]16 posts[/B]

Kristen and Julia went skating. Julia skated 30 minutes longer than Kristen. If Julia skated for 55 minutes, write and solve an equation to find how long Kristen skated Let j be the number of minutes Julia skates and k be the number of minutes Kristen skated. We have 2 equations: [B](1) j = k + 30 (2) j = 55[/B] [U]Plug (2) into (1)[/U] j = 55 + 30 [B]j = 85 minutes, or 1 hour and 25 minutes[/B]

Krutika was thinking of a number. Krutika doubles it and adds 8.7 to get an answer of 64.9. Form an equation with x from the information. [LIST=1] [*]The number we start with is x. [*]Double it means we multiply by 2: 2x [*]Add 8.7: 2x + 8.7 [*][I]Get an answer[/I] means we have an equation, so we set (3) above equal to 64.9 [*][B]2x + 8.7 = 64.9[/B] [/LIST] If you want to solve for x, use our [URL=' calculator[/URL].

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Lamar had N record albums that he tried to sell at a garage sale for $5 each. If the number of record albums he didn't sell is called Q, how much money did Lamar get from record album sales? Sales = Price * (Albums had - Albums sold) [B]Sales = 5(N - Q)[/B]

Lanette walked forward 9 steps, backward 15 steps, forward 7 steps, and backward 8 steps. How many steps is lanette from where she started? We use (+) for forward steps and (-) for backward steps [LIST] [*]Forward 9, backward 15 is: +9 - 15 = -6 [*]Forward 7 steps is: -6 + 7 = +1 [*]Backward 8 steps = +1 - 8 = -7 [/LIST] Since negative is backward and positive is forward, we see Lanette is [B]7 steps backwards [/B]from her starting point.

larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2 numbers Declare Variables for each number: [LIST] [*]Let l be the larger number [*]Let s be the smaller number [/LIST] We're given two equations: [LIST=1] [*]l = s + 12 [*]l + s = 74 [/LIST] Equation (1) already has l solved for. Substitute equation (1) into equation (2) for l: s + 12 + s = 74 Solve for [I]s[/I] in the equation s + 12 + s = 74 [SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE] (1 + 1)s = 2s [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2s + 12 = + 74 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 12 and 74. To do that, we subtract 12 from both sides 2s + 12 - 12 = 74 - 12 [SIZE=5][B]Step 4: Cancel 12 on the left side:[/B][/SIZE] 2s = 62 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2s/2 = 62/2 s = [B]31[/B] To solve for l, we substitute in s = 31 into equation (1): l = 31 + 12 l = [B]43[/B]

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number? Declare variables for the 2 numbers: [LIST] [*]Let l be the larger number [*]Let s be the smaller number [/LIST] We're given two equations: [LIST=1] [*]l = s + 4 [*]l + s = 40 [/LIST] To get this problem in terms of the larger number l, we rearrange equation (1) in terms of l. Subtract 4 from each side in equation (1) l - 4 = s + 4 - 4 Cancel the 4's and we get: s = l - 4 Our given equations are now: [LIST=1] [*]s = l - 4 [*]l + s = 40 [/LIST] Substitute equation (1) into equation (2) for s: l + l - 4 = 40 Grouping like terms for l, we get: 2l - 4 = 40 Add 4 to each side: 2l - 4 + 4 = 40 + 4 Cancelling the 4's on the left side, we get 2l = 44 Divide each side of the equation by 2 to isolate l: 2l/2 = 44/2 Cancel the 2's on the left side and we get: l = [B]22[/B]

Larry is rolling two dice. His dad told him that he can skip doing the dishes that night unless he rolls double sixes. What is the probability that Larry will be able to skip doing the dishes? P(6, 6) = 1/6 * 1/6 = 1/36 P(Not 6,6) = 1 - 1/36 = [B]35/36[/B]

Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7% annual simple interest. If the total yearly interest from both accounts was $2,090, find the amount invested at each rate. Let x be the amount invested at 6%. Then 31000 - x is invested at 7%. We have the following equation: 0.06x + (31000 - x)0.07 = 2090 Simplify: 0.06x + 2170 - 0.07x = 2090 Combine like Terms -0.01x + 2170 = 2090 Subtract 2170 from each side -0.01x = -80 Divide each side by -0.01 x = [B]8000 [/B]at 6% Which means at 7%, we have: 31000 - 8000 = [B]23,000[/B]

Last week at the business where you work, you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items? Let n be the number of items. We have the following equations: Cost Function C(n) = n For n = 120, we have C(120) = 120 Revenue Function R(n) = 3n For n = 120, we have R(120) = 3(120) = 360 Profit = Revenue - Cost Profit = 360 - 120 Profit = [B]240[/B]

Last year I made $50,000 working for a company. This year everyone takes a 9% pay cut. Next year everyone is promised a 15% pay raise. How much will I make next year? [U]Calculate pay cut amount with 9% = 0.09:[/U] Pay cut amount = Current Salary * (1 - pay cut percent) Pay cut amount = 50000 * (1 - 0.09) Pay cut amount = 50000 * 0.91 Pay cut amount = 45500 [U]Calculate pay raise with 15% = 0.15[/U] Pay raise amount = Pay Cut Salary * (1 + pay raise percent) Pay raise amount = 45500 * (1 + 0.15) Pay raise amount = 45500 * 1.15 Pay raise amount = [B]52,325[/B]

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Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden or a round garden with the fencing. Laura did some calculations and found that a circular garden would give her 1380 more square feet than a square garden. How many feet of fencing were in the roll that Laura found? (Round to the nearest foot.) Feet of fencing = n Perimeter of square garden = n Each side of square = n/4 Square garden's area = (n/4)^2 = n^2/16 Area of circle garden with circumference = n is: Circumference = pi * d n = pi * d Divide body tissues by pi: d = n/pi Radius = n/2pi Area = pi * n/2pi * n/2pi Area = pin^2/4pi^2 Reduce by canceling pi: n^2/4pi n^2/4 * 3.14 n^2/12.56 The problem says that the difference between the square's area and the circle's area is equal to 1380 square feet. Area of Circle - Area of Square = 1380 n^2/12.56 - n^2/16 = 1380 Common denominator = 200.96 (16n^2 - 12.56n^2)/200.96 = 1380 3.44n^2/200.96 = 1380 Cross multiply: 3.44n^2 = 277,324.8 n^2 = 80,617.7 n = 283.9 Nearest foot = [B]284[/B]

Laura weighs 45 pounds more than her pet dog. When they are on the scale together, they weigh 85 pounds. How much does Laura weigh? Let Laura weigh l and her dog weigh d. WE have: [LIST=1] [*]l = d + 45 [*]d + l = 85 [/LIST] Substitute equation (1) into Equation (2) for l: d + d + 45 = 85 Solve for [I]d[/I] in the equation d + d + 45 = 85 [SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE] (1 + 1)d = 2d [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2d + 45 = + 85 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 45 and 85. To do that, we subtract 45 from both sides 2d + 45 - 45 = 85 - 45 [SIZE=5][B]Step 4: Cancel 45 on the left side:[/B][/SIZE] 2d = 40 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2d/2 = 40/2 d = 20 From equation (1), we substitute d = 20: l = d + 45 l = 20 + 45 l = [B]65 pounds [URL='

Leah is 12 years older than Anna. if the age of Anna is x, what is the age of Leah? Older means we add 12 to Anna's age. So if Anna's age is x, then Leah's age (l) is: l = [B]x + 12[/B]

Leifs rich uncle decided to give him $1.00 the first day of Christmas and to double the amount each subsequent day. How much money (in dollars) does he recieve after all 12 days of Christmas? Let's look at each day: [LIST=1] [*]1 [*]2 [*]4 [*]8 [*]16 [*]32 [*]64 [*]128 [*]256 [*]512 [*]1024 [*]2048 [/LIST] Total received: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 = [B]4,095[/B]

Leilani can read 20 pages in 2 minutes. if she can maintain this page, how many pages can she read in an hour? We know that 1 hour is 60 minutes. Let p be the number of pages Leilani can read in 1 hour (60 minutes) The read rate is constant, so we can build a proportion. 20 pages /2 minutes = p/60 We can cross multiply: Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2 [SIZE=5][B]Solving for Numerator 2 we get:[/B][/SIZE] Numerator 2 = Numerator 1 * Denominator 2/Denominator 1 [SIZE=5][B]Evaluating and simplifying using your input values we get:[/B][/SIZE] p = 20 * 60/ 2 p = 1200/2 p = [B]600[/B]

Length (l) is the same as width (w) and their product is 64. We're given 2 equations: [LIST=1] [*]lw = 64 [*]l = w [/LIST] Substitute equation (2) into equation (1): w * w = 64 w^2 = 64 [B]w = 8[/B] Since l = w, then [B]l = 8[/B]

Leo and Zach went to lunch at a cafe. They ordered a spinach salad for $6.55, a tuna sandwich for $4.75, and 2 glasses of lemonade for $0.85 each. The tax was $1.30. They gave the waiter $15.00. How much change should they have received? Change = Cash - Total Bill - Tax Change = $15 - ($6.55 + $4.75 + 2($0.85)) - $1.30 Change = $15 - ($6.55 + $4.75 + $1.70) - $1.30 Change = $15 - $13 - $1.30 Change = $15 - $14.30 Change = [B]$0.70 or 70 cents[/B]

Leonard earned $100 from a bonus plus $15 per day (d) at his job this week. Which of the following expressions best represents Leonards income for the week? We set up an income function I(d), were d is the number of days Leonard works: [B]I(d) = 15d + 100 [/B] Each day, Leonard earns $15. Then we add on the $100 bonus

Let A = (-4,5) and B = (1,3) Find the distance from A to B Using our [URL=' between two points calculator[/URL], we get: [B]5.3852[/B]

Let A and B be independent events with P(A) = 0.52 and P(B) = 0.62. a. Calculate P(A ? B). With independent events, the intersection probability is found by: P(A ? B) = P(A) * P(B) P(A ? B) = 0.52 * 0.62 P(A ? B) = [B]0.3224[/B]

Let f(x) = 3x - 6 and g(x)= -2x + 5. Which of the following is f(x) - g(x)? f(x) - g(x) = 3x - 6 - (-2x + 5) Distribute the negative sign where double negative equals a plus: f(x) - g(x) = 3x - 6 + 2x - 5 Combine like terms: f(x) - g(x) = (3 + 2)x - 6 - 5 f(x) - g(x) = [B]5x - 11[/B]

Let f(x) = x - 2 and g(x) = x^2 + 7x - 3. Find f(g(-1)). g(-1) = -1^2 + 7(-1) - 3 g(-1) = 1 - 7 - 3 g(-1) = -9 f(-9) = -9 - 2 f(-9) = [B]-11[/B]

Let f(x)=5x and g(x)=2x + 1; find and simplify the following f(g(x)) f(g(x)) = 5(g(x)) f(g(x)) = 5(2x + 1) f(g(x)) = [B]10x + 5[/B]

Let n be an integer. If n^2 is odd, then n is odd Proof by contraposition: Suppose that n is even. Then we can write n = 2k n^2 = (2k)^2 = 4k^2 = 2(2k) so it is even [I]So an odd number can't be the square of an even number. So if an odd number is a square it must be the square of an odd number.[/I]

Let n be the middle number of three consecutive integers This means: [LIST] [*]n is the second of three consecutive integers [*]The first consecutive integer is n - 1 [*]The third consecutive integer is n + 1 [/LIST] The sum is found by: n - 1 + n + n + 1 Simplifying, we get: (n + n + n) + 1 - 1 [B]3n[/B]

Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What could N be? Is there more than one answer? For example, for 23 P(23) = 6 and S(23) = 5, but 23 could not be the N that we want since 23 <> 5 + 6 Let t = tens digit and o = ones digit P(n) = to S(n) = t + o P(n) + S(n) = to + t + o N = 10t + o Set them equal to each other N = P(N) + S(N) 10t + o = to + t + o o's cancel, so we have 10t = to + t Subtract t from each side, we have 9t = to Divide each side by t o = 9 So any two-digit number with 9 as the ones digit will work: [B]{19,29,39,49,59,69,79,89,99}[/B]

Let U be the set of all integers between ?3 and 3 (including ?3 and 3). Let A={?2,0,1,3}. Find Ac. Give your answer in standard set notation Ac is anything not in A, but in U. So we have: Ac = [B]{-3, -1, 2}[/B]

Let x be an integer. If x is odd, then x^2 is odd Proof: Let x be an odd number. This means that x = 2n + 1 where n is an integer. [U]Squaring x, we get:[/U] x^2 = (2n + 1)^2 = (2n + 1)(2n + 1) x^2 = 4n^2 + 4n + 1 x^2 = 2(2n^2 + 2n) + 1 2(2n^2 + 2n) is an even number since 2 multiplied by any integer is even So adding 1 is an odd number [MEDIA=youtube]GlzV80M33x0[/MEDIA]

License plates are made using 3 letters followed by 3 digits. How many plates can be made of repetition of letters and digits is allowed We have 26 letters in the alphabet We have 10 digits [0-9] The problem asks for the following license plate scenario of Letters (L) and Digits (D) LLLDDD The number of plates we can make using L = 26 and D = 10 using the fundamental rule of counting is: Number of License Plates = 26 * 26 * 26 * 10 * 10 * 10 Number of License Plates = [B]17,576,000[/B]

Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI with the following monthly billing policies. Each company's monthly billing policy has an initial operating fee and charge per megabyte. Operating Fee charge per Mb CIVSIN 29.95 0.14 GOMI 4.95 0.39 (i) Write down a system of equations to model the above situation (ii) At how many Mb is the monthly cost the same? What is the equal monthly cost of the two plans? (i) Set up a cost function C(m) for CIVSIN where m is the number of megabytes used: C(m) = charge per Mb * m + Operating Fee [B]C(m) = 0.14m + 29.95[/B] Set up a cost function C(m) for GOMI where m is the number of megabytes used: C(m) = charge per Mb * m + Operating Fee [B]C(m) = 0.39m + 4.95 [/B] (ii) At how many Mb is the monthly cost the same? Set both cost functions equal to each other: 0.14m + 29.95 = 0.39m + 4.95 We [URL=' this equation into our search engine[/URL] and we get: m = [B]100[/B] (ii) What is the equal monthly cost of the two plans? CIVSIN - We want C(100) from above where m = 100 C(100) = 0.14(100) + 29.95 C(100) = 14 + 29.95 C(100) = [B]43.95[/B] GOMI - We want C(100) from above where m = 100 C(100) = 0.39(100) + 4.95 C(100) = 39 + 4.95 C(100) = [B]43.95[/B]

Line m passes through points (3, 16) and (8, 10). Line n is perpendicular to m. What is the slope of line n? First, find the slope of the line m passing through points (3, 16) and (8, 10). [URL=' the points into our search engine[/URL], we get a slope of: m = -6/5 If line n is perpendicular to m, then the slope of n is denote as: n = -1/m n = -1/-6/5 n = -1*-5/6 n = [B]5/6[/B]

Line m passes through points (7, 5) and (9, 10). Line n passes through points (3, 1) and (7, 10). Are line m and line n parallel or perpendicular [U]Slope of line m is:[/U] (y2 - y1)/(x2 - x1) (10 - 5)/(9 - 7) 5/2 [U]Slope of line n is:[/U] (y2 - y1)/(x2 - x1) (10 - 1)/(7 - 3) 9/4 Run 3 checks on the slopes: [LIST=1] [*]Lines that are parallel have equal slopes. Since 5/2 does not equal 9/4, these lines [B]are not parallel[/B] [*]Lines that are perpendicular have negative reciprocal slopes. Since 9/4 is not equal to -2/5 (the reciprocal of the slope of m), these lines [B]are not perpendicular[/B] [*][B]Therefore, since the lines are not parallel and not perpendicular[/B] [/LIST]

Free Linear Congruence Calculator - Given an modular equation ax ≡ b (mod m), this solves for x if a solution exists

Free Liquid Conversions Calculator - Takes a liquid measurement as seen in things like recipes and performs the following conversions: ounces, pints, quarts, gallons, teaspoon (tsp), tablespoon (tbsp), microliters, milliliters, deciliters, kiloliters,liters, bushels, and cubic meters.

Lisa wants to rent a boat and spend less than $52. The boat costs $7 per hour, and Lisa has a discount coupon for $4 off. What are the possible numbers of hours Lisa could rent the boat? Calculate discounted cost: Discounted cost = Full Cost - Coupon Discounted cost = 52 - 7 Discounted cost = 45 Since price equals rate * hours (h), and we want the inequality (less than) we have: 7h < 52 Using our [URL=' calculator,[/URL] we see that: [B]h < 7.42[/B]

Free Littles Law Calculator - Given two out of the three inputs for Littles Law, Throughput (TH), Cycle Time (CT, and WIP, this solves for the third item.

Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes. If the total value of the coins is 2.18, how many of each denomination does she have? [U]Set up two equations where p is the number of pennies and d is the number of dimes:[/U] (1) d + p = 47 (2) 0.1d + 0.01p = 2.18 [U]Rearrange (1) into (3) by solving for d[/U] (3) d = 47 - p [U]Substitute (3) into (2)[/U] 0.1(47 - p) + 0.01p = 2.18 4.7 - 0.1p + 0.01p = 2.18 [U]Group p terms[/U] 4.7 - 0.09p = 2.18 [U]Add 0.09p to both sides[/U] 0.09p + 2.18 = 4.7 [U]Subtract 2.18 from both sides[/U] 0.09p = 2.52 [U]Divide each side by 0.09[/U] [B]p = 28[/B] [U]Now substitute that back into (3)[/U] d =47 - 28 [B]d = 19[/B]

Local salesman receives a base salary of $650 monthly. He also receives a commission of 11% on all sales over $1500. How much would he have to sell in one month if he needed to have $3000 Let the Sales amount be s. We have: Sales over 1,500 is written as s - 1500 11% is also 0.11 as a decimal, so we have: 0.11(s - 1500) + 650 = 3000 Multiply through: 0.11s - 165 + 650 = 3500 0.11s + 485 = 3500 To solve this equation for s, [URL=' type it in our search engine[/URL] and we get: s = [B]27,409.10[/B]

log5 = 0.699, log2 = 0.301. Use these values to evaluate log40. One of the logarithmic identities is: log(ab) = log(a) + log(b). Using the numbers 2 and 5, we somehow need to get to 40. [URL=' factors of 40[/URL]. On the link above, take a look at the bottom where it says prime factorization. We have: 40 = 2 x 2 x 2 x 5 Using our logarithmic identity, we have: log40 = log(2 x 2 x 2 x 5) Rewriting this using our identity, we have: log40 = log2 + log2 + log2 + log5 log40 = 0.301 + 0.301 + 0.301 + 0.699 log40 = [B]1.602 [MEDIA=youtube]qyG_Jkf9VDc[/MEDIA][/B]

Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nephew? Let the age of Logan's nephew be n. We're given: 4n + 8 = 32 (Since [I]older[/I] means we add) To solve this equation for n, we [URL=' it into our search engine[/URL] and we get: [B]n = 6[/B]

Free Logarithms Calculator - Using the formula Log a_b = e, this calculates the 3 pieces of a logarithm equation:1) Base (b)2) Exponent3) Log Result In addition, it converts * Expand logarithmic expressions

Free Logistic Map Calculator - Given r, x₀ and (n) trials, this will display the logistic map.

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Lucy is thinking of a number. The number is greater than two hundred twenty-five. Her number is less than 2 hundreds, 2 tens, and 7 ones. What is Lucy's number? Let the number be n. n > 225 Also: n < 2(100) + 2(10) + 7(1) n < 200 + 20 + 7 n < 227 Combine these, we get: 225 < n < 227 Only one number satisfies this: n = [B]226 [MEDIA=youtube]-LFbAZFy13o[/MEDIA][/B]

Luke and Dan's total debt is $72. If Luke's debt is three times Dan's debt, what is Dan's debt? Let Dan's debt be d. Let Luke's debt be l. We're given two equations: [LIST=1] [*]d + l = 72 [*]l = 3d [/LIST] Substitute equation (2) for l into equation (1): d + 3d = 72 Solve for [I]d[/I] in the equation d + 3d = 72 [SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE] (1 + 3)d = 4d [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 4d = + 72 [SIZE=5][B]Step 3: Divide each side of the equation by 4[/B][/SIZE] 4d/4 = 72/4 d = [B]18[/B]

M decreased by the sum of 13 and the number P is less than 12 The sum of 13 and the number P 13 + P M decreased by the sum of 13 and the number P M - (13 + P) Less than 12 means we set this entire expression less than 12 as an inequality [B]M - (13 + P) < 12[/B]

m is inversely proportional to the square of p-1 when p=4 and m=5. find m when p=6 Inversely proportional means there is a constant k such that: m = k/(p - 1)^2 When p = 4 and m = 5, we have: 5 = k/(4 - 1)^2 5 = k/3^2 5 = k/9 [U]Cross multiply:[/U] k = 45 [U]The problems asks for m when p = 6. And we also now know that k = 45. So plug in the numbers:[/U] m = k/(p - 1)^2 m = 45/(6 - 1)^2 m = 45/5^2 m = 45/25 m = [B]1.8[/B]

M is the midpoint of AB. Prove AB = 2AM M is the midpoint of AB (Given) AM = MB (Definition of Congruent Segments) AM + MB = AB (Segment Addition Postulate) AM + AM = AB (Substitution Property of Equality) 2AM = AB (Distributive property) [MEDIA=youtube]8BNo_4kvBzw[/MEDIA]

m is the midpoint of cf for points c(3,4) and f(9,8). Find MF Using our [URL=' equation and midpoint calculator[/URL], we get: MF = [B](6, 6)[/B]

M is the set of integers that are greater than or equal to -1 and less than or equal to 2 We include -1 on the left, and include 2 on the right [B]M = {-1, 0, 1, 1, 2)[/B]

m times the difference of 2p and 4r The difference of 2p and 4r: 2p - 4r m times the difference: [B]m(2p - 4r)[/B]

Sum of n and 5 n + 5 m times that sum m(n + 5)

M/n = p-6 for m Solve this literal equation by multiplying each side by n to isolate M: Mn/n = n(p - 6) Cancelling the n terms on the left side, we get: [B]M = n(p - 6)[/B]

m/x = k-6 for m To solve this literal equation, multiply each side by x: x(m/x) = x(k - 6) The x's cancel on the left side, so we get: m = [B]x(k - 6)[/B]

m=u/k-r/k for k Multiply both sides by k to eliminate the k denominator: km = uk/k - rk/k Cancel the k's on the right side and we get km = u - r Divide each side by m: km/m = (u - r)/m Cancel the m on the left side: [B]k = (u - r)/m[/B]

Madelines science quiz consists of 10 questions, all of which are true or false. How many different choices for answering the 10 questions are possible? 2 ways of answering each True or False Question ^ (10 different ways to answer each question) 2^10 = [B]1,024 ways[/B]

Maggie earns $10 each hour she works at the pet store and $0.25 for each phone call she answers. Maggie answered 60 phone calls and earned $115 last week Set up an equation where c is the number of phone calls Maggie answers and h is the number of hours Maggie worked: 0.25c + 10h = 115 We're given c = 60, so we have: 0.25(60) + 10h = 115 15 + 10h = 115 We want to solve for h. So we[URL=' type this equation into our search engine[/URL] and we get: h = [B]10[/B]

Free MAPE - MPE - MAPD Calculator - Given a time series of actual and forecasted values, this determines the following: * Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD) * Symmetric Mean Absolute Percentage Error (sMAPE) * Mean Absolute Percentage Error (MPE)

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is the area of one piece? A pizza is a circle. If the diameter of the pizza is 14 inches, the radius is 14/2 = 7 inches. Area of a circle is pi(r^2). With r = 7, we have: A =7^2(pi) A = 49pi Area of a slice of pizza is the area of the full pizza divided by 8 A(Slice) = [B]49pi/8[/B]

Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of weeks x and the total number of quizzes y. Write your answer as an equation with y first, followed by an equals sign. Our total quizzes equal 2 times the number of weeks (x): [B]y = 2x[/B]

Maria bought 7 boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start? [U]Let x be the starting box number. We have:[/U] (x + 7)/2 = 22 [U]Cross multiply[/U] x + 7 = 44 [U]Subtract 7 from each side[/U] [B]x = 37[/B]

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. How many did she start with? Take this in parts [LIST=1] [*]Maria starts with b boxes. [*]She buys seven more. So she has b + 7 boxes [*]A week later, half of all her boxes are destroyed in a fire. Which means she's left with 1/2. (b + 7)/2 [*]Now she has 22 boxes. So we set (b + 7)/2 = 22 [/LIST] (b + 7)/2 = 22 Cross multiply: b + 7 = 22 * 2 b + 7 = 44 [URL=' this equation into our search engine and solving for b[/URL], we get: [B]b = 37[/B]

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start? Let the number of boxes Maria started with be b. We're given the following pieces: [LIST] [*]She starts with b [*]She bought 7 boxes. So we add 7 to b: b + 7 [*]If half the boxes were destroyed, she's left with 1/2. So we divide (b + 7)/2 [*]Only 22 boxes left means we set (b + 7)/2 equal to 22 [/LIST] (b + 7)/2 = 22 Cross multiply: b + 7 = 22 * 2 b + 7 = 44 [URL=' this equation into our search engine[/URL] to solve for b and we get: b = [B]37[/B]

Maria called her sister long distance on Wednesday. The first 5 minutes cost $3, and each minute after that cost $0.25. How much did it cost if they talked for 15 minutes? First 5 minutes: $3 If they talked 15 minutes, the additional charge past 5 minutes is: 0.25 * (15 - 5) 0.25 * 10 minutes = $2.5 We add this to the first 5 minutes: $3 + $2.5 = [B]$5.50[/B]

Maria paid a fee of $75 to the local golf course. For every 18 holes of goals it was $12.50. How much did Maria pay to play 36 holes of golf 36 holes is 2 * 18 hole rounds. [U]Maria's total cost for the trip is:[/U] Maria's Fee = Local Golf Course Fee + 2(18 hole round fee) Maria's Fee = 75 + 2(12.50) Maria's Fee = 75 +25 Maria's Fee = [B]$100[/B]

Let n be the number of nickels and q be the number of quarters. We have two equations: (1) n + q = 24 (2) 0.05n + 0.25q = 3 Rearrange (1) to solve for n in terms of q for another equation (3) (3) n = 24 - q Plug (3) into (2) 0.05(24 - q) + 0.25q = 3 Multiply through: 1.2 - 0.05q + 0.25q = 3 Combine q terms 0.2q + 1.2 = 3 Subtract 1.2 from each side: 0.2q = 1.8 Divide each side by 0.2 [B]q = 9[/B]

Mark and Jennie are bowling. Jennies score is double Marks score. If the sum of their score is 171, find each persons score by writing out an equation. Let Mark's score be m. Let Jennie's score be j. We're given two equations: [LIST=1] [*]j = 2m [*]j + m = 171 [/LIST] Substitute equation (1) into equation (2): 2m + m = 171 [URL=' this equation into our search engine[/URL] to solve for m: m = [B]57 [/B] To solve for j, we substitute m = 57 in equation (1) above: j = 2(57) j = [B]114[/B]

mark has a drawer full of 12 yellow baseball caps and 18 white baseball caps. What is the probability of the next cap he chooses at random will be yellow? P(yellow) = yellow caps / Total caps P(yellow) = 12/(12 + 18) P(yellow) = 12/30 [URL=' this fraction,[/URL] we get: P(yellow) = [B]2/5[/B]

Marla wants to rent a bike Green Lake Park has an entrance fee of $8 and charges $2 per hour for bike Oak Park has an entrance fee of $2 and charges $5 per hour for bike rentals she wants to know how many hours are friend will make the costs equal [U]Green Lake Park: Set up the cost function C(h) where h is the number of hours[/U] C(h) = Hourly Rental Rate * h + Entrance Fee C(h) = 2h + 8 [U]Oak Park: Set up the cost function C(h) where h is the number of hours[/U] C(h) = Hourly Rental Rate * h + Entrance Fee C(h) = 5h + 2 [U]Marla wants to know how many hours make the cost equal, so we set Green Lake Park's cost function equal to Oak Parks's cost function:[/U] 2h + 8 = 5h + 2 To solve for h, we [URL=' this equation into our search engine[/URL] and we get: h = [B]2[/B]

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find the ages of Martha and Harry. Let m be Martha's age. Let h be Harry's age. We're given two equations: [LIST=1] [*]m = h + 18 [I](older means we add)[/I] [*]h + m = 106 [/LIST] Substitute equation (1) into equation (2) for m: h + h + 18 = 106 To solve for h, [URL=' type this equation into our search engine[/URL] and we get: h = [B]44[/B]

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than 11. What is the youngest age Warren can be? Let m be Marty's age and w be Warren's age. We have two equations: (1) m = 6w - 3 (2) m + w > 11 Plug (1) into (2) 6w - 3 + w > 11 Combine w terms 7w - 3 > 11 Add 3 to each side 7w > 14 Divide each side by 7 w > 2 which means [B]w = 3[/B] as the youngest age.

Mary owns a store that sells computers. Her profit in dollars is represented by the function P(x) = x^3 - 22x^2 - 240x, where x is the number of computers sold. Mary hopes to make a profit of at least $10,000 by the time she sells 36 computers. Explain whether Mary will meet her goal. Justify your reasoning. Calculate P(10): P(10) = 10^3 - 22(10)^2 - 240(10) P(10) = 1000 - 2200 - 2400 P(10) = -3600 Mary will [B]not[/B] meet her goal of making a profit of at least $10,000 when she sells 36 computers because her profit is in the negative.

Match each variable with a variable by placing the correct letter on each line. a) principal b) interest c) interest rate d) term/time 2 years 1.5% $995 $29.85 [B]Principal is $995 Interest is $29.85 since 995 * .0.15 * 2 = 29.85 Interest rate is 1.5% Term/time is 2 year[/B]s

Volume of rectangular prism is: V = lwh Plugging in the numbers you gave: 195 = (6)(5)h 195 = 30h Divide each side by 30 h = 6.5 6.5 feet is 6 feet, 6 inches. This is 2 inches more than your actor, so [B]yes[/B], he will fit in the box standing up.

Im sorta confused about this question? He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this. Here is (most of) the information you asked for: [LIST] [*]Is he redoing the whole yard or just the front? He's redoing the whole yard [*]How much topsoil does he need? I'm not sure, you'll have to figure that out. Remember he's putting a new 4 inch layer down over all the area currently covered by grass in the overhead picture above. [*]How big is the yard? I'm not sure, but you can probably estimate it using the overhead picture. [*]What kind of pickup truck does he drive? A 2003 Ford F-150 XL. [*]How much can the pickup carry? The truck bed is 80 inches long, 69 inches wide, and 20 inches tall. [*]How much is the delivery charge? $30 per truckload on top of the soil cost. Each truckload can deliver up to 18 cubic yards. [*]How much does the topsoil cost? $18 per cubic yard (sold in 1/4 yard increments). [*]How far is the soil store? It is 9 miles away. It takes about 20 minutes to drive there. [*]What gas mileage does the pickup truck get? It averages 17 miles to the gallon. [*]What is the current gas cost? Assume it's $3.79/gallon. [/LIST] Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery? Detail all your assumptions and calculations, and clearly write out your final conclusions.

Free Matrix Properties Calculator - Given a matrix |A|, this calculates the following items if they exist:* Determinant = det(A)* Inverse = A^-1* Transpose = A^T* Adjoint = adj(A)* Eigen equation (characteristic polynomial) = det|λI - A|* Trace = tr(A) * Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form * Dimensions of |A| m x n * Order of a matrix * Euclidean Norm ||A|| * Magic Sum if it exists * Determines if |A| is an Exchange Matrix

Matt has $100 dollars in a checking account and deposits $20 per month. Ben has $80 in a checking account and deposits $30 per month. Will the accounts ever be the same balance? explain Set up the Balance account B(m), where m is the number of months since the deposit. Matt: B(m) = 20m + 100 Ben: B(m) = 80 + 30m Set both balance equations equal to each other to see if they ever have the same balance: 20m + 100 = 80 + 30m To solve for m, [URL=' type this equation into our search engine[/URL] and we get: m = [B]2 So yes, they will have the same balance at m = 2[/B]

Matthew's cat weighs 10 pounds more than his pet hamster. His dog weighs the same as his cat. If the weight of all three pets is 35 pounds, ow much does his hamster weigh? Setup weights and relations: [LIST] [*]Hamster weight: w [*]Cat weight: w + 10 [*]Dog weight:w + 10 [/LIST] Add all the weights up: w + w + 10 + w + 10 = 35 Solve for [I]w[/I] in the equation w + w + 10 + w + 10 = 35 [SIZE=5][B]Step 1: Group the w terms on the left hand side:[/B][/SIZE] (1 + 1 + 1)w = 3w [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] 10 + 10 = 20 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 3w + 20 = + 35 [SIZE=5][B]Step 4: Group constants:[/B][/SIZE] We need to group our constants 20 and 35. To do that, we subtract 20 from both sides 3w + 20 - 20 = 35 - 20 [SIZE=5][B]Step 5: Cancel 20 on the left side:[/B][/SIZE] 3w = 15 [SIZE=5][B]Step 6: Divide each side of the equation by 3[/B][/SIZE] 3w/3 = 15/3 w =[B] 5[/B] [B] [URL='

Matthew's pay increases by 20% each month. If his first pay is $450, determine the amount of his pay in month 5. Let me be the number of months. We have a pay functionalists P(m) as: P(m) = Initial Pay * (1 + Increase %/100)^m With m = 5, initial pay = 450, and Increase % = 20, we have P(5) = 450 * (1.2)^5 P(5) = 450 * 2.48832 P(5) = [B]1,119.74[/B]

Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00. Bob bought 3 burgers and 1 drink for $5.50. How much is each burger and drink? [U]Set up the givens where b is the cost of a burger and d is the cost of a drink:[/U] Max: 2b + 2d = 5 Bob: 3b + d = 5.50 [U]Rearrange Bob's equation by subtracting 3b from each side[/U] (3) d = 5.50 - 3b [U]Now substitute that d equation back into Max's Equation[/U] 2b + 2(5.50 - 3b) = 5 2b + 11 - 6b = 5 [U]Combine b terms:[/U] -4b + 11 = 5 [U]Subtract 11 from each side[/U] -4b = -6 [U]Divide each side by -4[/U] b = 3/2 [B]b = $1.50[/B] [U]Now plug that back into equation (3):[/U] d = 5.50 - 3(1.50) d = 5.50 - 4.50 [B]d = $1.00[/B]

Max is 23 years younger than his father.Together their ages add up to 81. Let Max's age be m, and his fathers' age be f. We're given: [LIST=1] [*]m = f - 23 <-- younger means less [*]m + f = 81 [/LIST] Substitute Equation (1) into (2): (f - 23) + f = 81 Combine like terms to form the equation below: 2f - 23 = 81 [URL=' this equation into our search engine[/URL], we get: [B]f = 52[/B] Substitute this into Equation (1): m = 52 - 23 [B]m = 29[/B]

Max sneezes every 5 minutes, Lina coughs every 6 minutes, and their dog barks every 3 minutes. If there was sneezing, barking, and coughing at 3:15 PM, when is the next time that these three sounds will happen simultaneously? To find the next time the sounds happen simultaneously, we want to find the Least Common Multiple (LCM). [URL=' our LCM Calculator[/URL], we find the least common multiple of 3, 5, and 6 is 30. The least common multiple gives us a common time where each sound reaches a "cycle". [LIST] [*]Dog: A bark every e minutes means the dog has 10 barks, with the 10th bark at 30 minutes after 3:15 [*]Max: A sneeze every 5 minutes means he has 6 sneezes, with the 6th sneeze at 30 minutes after 3:15 [*]Lisa: A cough every 6 minutes means she has 5 coughs, with the 5th cough at 30 minutes after 3:15 [/LIST] 30 minutes after 3:15 means we have: 3:15 + 30 = [B]3:45 PM[/B]

Max's age is 2 more than his fathers age divided by 4. Max is 13 years old. How old is his dad? Let Max's father be age f. We're given: (f + 2)/4 = 13 Cross Multiply: f + 2 = 52 [URL=' this equation into the search engine[/URL], we get: f = [B]50[/B]

Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many weeks will megan and connor have saved the same amount [U]Set up the Balance function B(w) where w is the number of weeks for Megan:[/U] B(w) = savings per week * w + Current Balance B(w) = 5.50w + 50 [U]Set up the Balance function B(w) where w is the number of weeks for Connor:[/U] B(w) = savings per week * w + Current Balance B(w) = 7.75w + 18.50 The problem asks for w when both B(w) are equal. So we set both B(w) equations equal to each other: 5.50w + 50 = 7.75w + 18.50 To solve this equation for w, we[URL=' type it in our search engine[/URL] and we get: w = [B]14[/B]

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she charges $53 for each lawn, how many lawns must she service to make a profit of at $800 a month? Melissa has a fixed cost of $264 per month in fuel. No variable cost is given. Our cost function is: C(x) = Fixed Cost + Variable Cost. With variable cost of 0, we have: C(x) = 264 The revenue per lawn is 53. So R(x) = 53x where x is the number of lawns. Now, profit is Revenue - Cost. Our profit function is: P(x) = 53x - 264 To make a profit of $800 per month, we set P(x) = 800. 53x - 264 = 800 Using our [URL=' solver[/URL], we get: [B]x ~ 21 lawns[/B]

Michelle and Julie sold 65 cupcakes. If Julie sold 9 more cupcakes than Michelle, how many cupcakes did each of them sell? Let m = Michelle's cupcakes and j = Julie's cupcakes. We have two equations: m + j = 65 j = m + 9 Substituting, we get: m + (m + 9) = 65 Combine like terms, we get: 2m + 9 = 65 Subtract 9 from each side: 2m = 56 Divide each side by 2 to isolate m m = 28 If m = 28, then j = 28 + 9 = 37 So (m, j) = (28, 37)

Michelle and Natalie both went out to eat at a new restaurant. Michelles bill was $22.50, and she left a 15% tip. Natalies bill was $24.25, and she left a 10% tip. Whose total bill was the greatest? [U]Michelles's total bill:[/U] Total Bill = Pre-Tax Bill * (1 + tax rate) Since 15% = 0.15, we have: Total Bill = 22.50 * 1.15 Total Bill = 25.88 [U]Natalie's total bill:[/U] Total Bill = Pre-Tax Bill * (1 + tax rate) Since 10% = 0.10, we have: Total Bill = 24.25 * 1.10 Total Bill = 26.68 [B]Natalie's[/B] total bill was the greatest.

Midpoint formula Given two points (x1, y1) and (x2, y2), the midpoint is found as the average distance between the 2 points: [LIST] [*]x value is: (x1 + x2)/2 [*]y value is: (y1 + y2)/2 [/LIST] So our midpoint is: ((x1 + x2)/2, (y1 + y2)/2)

Miguel has $80 in his bank and saves $2 a week. Jesse has $30 in his bank but saves $7 a week. In how many weeks will Jesse have more in his bank than Miguel? [U]Set up the Bank value B(w) for Miguel where w is the number of weeks[/U] B(w) = Savings Per week * w + Current Bank Balance B(w) = 2w + 80 [U]Set up the Bank value B(w) for Jesse where w is the number of weeks[/U] B(w) = Savings Per week * w + Current Bank Balance B(w) = 7w + 30 The problem asks when Jesse's account will be more than Miguel's. So we set up an inequality where: 7w + 30 > 2w + 80 To solve this inequality, we [URL=' it in our search engine[/URL] and we get: [B]w > 10[/B]

mike went to canalside with $40 to spend. he rented skates for $10 and paid $3 per hour to skate.what is the greatest number of hours Mike could have skated? Let h be the number of hours of skating. We have the cost function C(h): C(h) = Hourly skating rate * h + rental fee C(h) = 3h + 10 The problem asks for h when C(h) = 40: 3h + 10 = 40 To solve this equation for h, we [URL=' it in our search engine[/URL] and we get: h = [B]10[/B]

Mike works in a toy store. One week, he worked 38 hours and made $220. The next week, he received a raise, so when he worked 30 hours he made $180. How much was his raise (to the nearest cent)? First week, Mike earns the following in hours (h) 38h = 220 h = 5.79 [URL=' our equation calculator[/URL] We call this his old hourly salary Next week, Mike earns the following in hours (h) 30h = 180 h = 6 [URL=' our equation calculator[/URL] We call this his new hourly salary His raise is the difference between his current hourly salary and his old hourly salary: Raise = New Hourly Salary - Old Hourly Salary Raise = 6 - 5.79 Raise = [B]$0.21[/B] Mike got a 21 cent hourly raise

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent's serves. Assume her opponent serves 8 times. Show all work. Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution. a) What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? b) Find the probability that that she returns at least 1 of the 8 serves from her opponent. (c) How many serves can she expect to return? a) [B]n = 8 p = 0.2[/B] q = 1 - p q = 1 - 0.2 [B]q = 0.8 [/B] b) [B]0.4967[/B] on our [URL=' calculator[/URL] c) np = 8(0.2) = 1.6 ~ [B]2[/B] using the link above

Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake and troy had 1/4 of the total cake. Write an equation to determine how many pieces of cake (c) that were in total Let c be the total number of pieces of cake. Let m be the number of pieces Mindy ate. Let t be the number of pieces Troy ate. We have the following given equations: [LIST] [*]m + t = 9 [*]m = 3 [*]t = 1/4c [/LIST] Combining (2) and (3) into (1), we have: 3 + 1/4c = 9 Subtract 3 from each side: 1/4c = 6 Cross multiply: [B]c = 24 [MEDIA=youtube]aeqWQXr5f_Y[/MEDIA][/B]

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Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water as juice. How many ounces of strawberry juice and how many ounces of water does she need to make 40 ounces of strawberry infused water? Let j be the ounces of strawberry juice and w be the ounces of water. We're given: [LIST=1] [*]j + w = 40 [*]w = 3j [/LIST] Substitute (2) into (1): j + 3j = 40 Combine like terms: 4j = 40 [URL=' this equation into our search engine[/URL], we get: [B]j = 10[/B] From equation (2), we substitute j = 2: w = 3(10) [B]w = 30 [/B] This means we have [B]10 ounces of juice[/B] and [B]30 ounces of water[/B] for a 40 ounce mix.

Free Moment of Inertia Calculator - Calculates any of the 3 items from the Moment of Inertia equation, Inertia (I), Mass (M), and Length (L).

Mr turner sent his car to the workshop for repair work as well as to change 4 tires. Mr turner paid $1035 in all. The repair work cost 5 times the price of each tire. The mechanic told Mr. turner that the repair work cost $500. Explain the mechanics mistake Let the cost for work be w. Let the cost for each tire be t. We're given; [LIST=1] [*]w = 5t [*]w + 4t = 1035 [/LIST] Substitute equation 1 into equation 2: (5t) + 4t = 1035 [URL=' this equation into our search engine[/URL], and we get: t = 115 Substitute this into equation (1): w = 5(115) w = [B]575[/B] The mechanic underestimated the work cost.

Mr. Chriss new app Tick-Tock is the hottest thing to hit the app store since...ever. It costs $5 to buy the app and then $2.99 for each month that you subscribe (a bargain!). How much would it cost to use the app for one year? Write an equation to model this using the variable m to represent the number of months that you use the app. Set up the cost function C(m) where m is the number of months you subscribe: C(m) = Monthly Subscription Fee * months + Purchase fee [B]C(m) = 2.99m + 5[/B]

Mr. Demerath has a large collection of Hawaiian shirts. He currently has 42 Hawaiian shirts. He gets 2 more every month. After how many months will Mr. Demerath have at least 65 Hawaiian shirts? We set up the function H(m) where m is the number of months that goes by. Mr. Demerath's shirts are found by: H(m) = 2m + 42 The problem asks for m when H(m) = 65. So we set H(m) = 65: 2m + 42 = 65 To solve this equation for m, we[URL=' type it in our search engine [/URL]and we get: m = [B]11.5[/B]

Mr. Elk is secretly a huge fan of Billie Eilish, and is saving up for front row seats. He puts $250 in the bank that has an interest rate of 8% compounded daily. After 4 years, Billie is finally hitting up NJ on her tour. How much money does Mr. Elk have in the bank? (rounded to the nearest cent) * 4 years = 365*4 days 4 years = 1,460 days. Using this number of compounding periods, we [URL=' this into our compound interest calculator[/URL] to get: [B]$344.27[/B]

Mr. Jimenez has a pool behind his house that needs to be fenced in. The backyard is an odd quadrilateral shape and the pool encompasses the entire backyard. The four sides are 1818a, 77b, 1111a, and 1919b in length. How much fencing? (the length of the perimeter) would he need to enclose the pool? The perimeter P is found by adding all 4 sides: P = 1818a + 77b + 1111a + 1919b Group the a and b terms P = (1818 + 1111)a + (77 + 1919b) [B]P = 2929a + 1996b[/B]

Mr. Smith wants to spend less than $125 at a zoo. A ticket cost $7 he is taking 2 kids with him. Use p to represent the other money he can spend there. 2 kids and Mr. Smith = 3 people. Total Ticket Cost is 3 people * 7 per ticket = 21 If he has 125 to spend, we have the following inequality using less than or equal to (<=) since he can spend up to or less than 125: p + 21 <= 125 Subtract 21 from each side: [B]p <= 104[/B]

Mr. Winkle downloaded 34 more songs than Mrs. Winkle downloaded. Together they downloaded 220 songs. How many songs did each download? Let x = Mr. Winkle downloads and y = Mrs. Winkle downloads. We then have x = y + 34 and x + y = 220. Substitute equation 1 into equation 2, we have: (y + 34) + y = 220 2y + 34 = 220 Subtract 34 from each side: 2y = 186 Divide each side by 2: y = 93 (Mrs. Winkle) x = 93 + 34 x = 127 (Mr. Winkle)

Mrs. Evans has 120 crayons and 30 pieces of paper to give her students. What is the largest number of students she can have her class so that each student gets an equal number of crayons and equal number of paper? [URL=' our GCF calculator for the GCF(30, 120)[/URL], we get 30. So 30 people get the following: [B]30/30 = 1 piece of paper 120/30 = 4 crayons[/B]

Mrs. Lopez gave a homework assignment over summer vacation to read three books from the following list: a) Call of the Wild b) Wuthering Heights c) Death of a Salesman d) The Cartoon Book of Physics How many possible combinations of three books are there in the list of four books? We need to elimination those of the same order, so we use combinations: [URL=' = [B]4[/B]

Mrs. Taylor is making identical costumes for the dancers in the dance club. She uses 126 pink ribbons and 108 yellow ribbons. a) What is the maximum possible number of costumes she can make? b) How many pink and how many yellow ribbons are on each costume? a), we want the greatest common factor (GCF) of 108 and 126. [URL=' our GCF calculator[/URL] we get: [B]a) 18 costumes [/B] b) Pink Ribbons per costume = Total Pink Ribbons / GCF in question a Pink Ribbons per costume = 126/18 Pink Ribbons per costume = [B]7[/B] [B][/B] Yellow Ribbons per costume = Total Yellow Ribbons / GCF in question a Yellow Ribbons per costume = 108/18 Yellow Ribbons per costume = [B]6[/B]

Ms. Gonzales is investing $17000 at an annual interest rate of 6% compounded continuously. How much money will be in the account after 16 years? Round your answer to the nearest hundredth (two decimal places). Using our [URL=' interest calculator[/URL], we get: [B]44,398.84[/B]

Ms. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngest and the middle son gets $35 more than the youngest, how much does each boy get? Let 0 be the oldest son, m be the middle sun, and y be the youngest son. Set up our given equations [LIST] [*]o = 2y [*]m = y + 35 [*]o + m + y = 975 [/LIST] [U]Substitute the first and second equations into Equation 3[/U] 2y + y + 35 + y = 975 [U]Combine the y terms[/U] 4y + 35 = 975 Subtract 35 using our [URL=' calculator[/URL] to solve and get [B]y = 235[/B] [U]Plug y = 235 into equation 2[/U] m = 235 + 35 [B]m = 270[/B] [U]Plug y = 235 into equation 2[/U] o = 2(235) [B]o = 470[/B]

Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations? Above sea level is listed as positive (+) Below sea level is listed as negative (-) We have: Difference = +29,028 - (-1312) Difference = 29028 + 1312 [URL=' = [B]30,340[/B]

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Free Multiple Fractions (Addition or Ordering) Calculator - This adds 3 or more fractions or arranges a list of fractions from lowest to highest and highest to lowest (ordering fractions or sorting fractions)

multiply 3 by the difference of u and t Take this algebraic expression in parts: The difference of u and t means we subtract t from u u - t Multiply this difference by 3: [B]3(u - t)[/B]

Multiply 3w by the sum of v and 2u the sum of v and 2u: v + 2u Multiply 3w by the sum of v and 2u [B]3w(v + 2u)[/B]

multiply 5 and sum of twice of d and 10 Twice d means we multiply d by 2: 2d The sum of twice d and 10 means we add 2d to 10 2d + 10 We multiply this quantity by 5: [B]5(2d + 10)[/B]

multiply 9 by the quotient of 4 and z Quotient of 4 and z is written as: 4/z Multiply this quotient by 9: 9(4)/z Multiplying the top, we get: [B]36/z[/B]

Multiply c by five and square the answer Multiply c by five: 5c Square the answer means we raise 5c to the power of 2: [B](5c)^2 [/B] This can also be written as [B]25c^2[/B]

multiply m by 5, double the result, then multiply 10 by what you have Take this algebraic expression in parts: [LIST] [*]Multiply m by 5: 5m [*]double the result means multiply 5m by 2: 2(5m) = 10m [*]Multiply 10 by what you have means multiply 10 by the result of 10m above: [/LIST] 10(10m) = [B]100m[/B]

multiply r by t, add the result to u, then multiply what you have by s Take this algebraic expression in parts: [LIST=1] [*]Multiply r by t: rt [*]Add the result to u means we add rt to u: u + r [*]Multiply what you have by s. This means we take the result in #2, u + r, and multiply it by s: [/LIST] [B]s(u + r)[/B]

multiply t by u, add the to v, then triple what you have Multiply t by u: tu Add this to v: v + tu Then triple what you have - This means we multiply the expression above by 3: [B]3(v + tu)[/B]

Multiply the difference of 3 and q by p. Take this algebraic expression in pieces: [B][U]Step 1: The difference of 3 and q[/U][/B] The word [I]difference[/I] means we subtract the variable q from 3 3 - q [B][U]Step 2: Multiply the expression 3 - q by p:[/U] p(3 - q)[/B]

multiply the sum of 2p and q by3 The sum of 2p and q: 2p + q Multiply the sum by 3: [B]3(2p + q)[/B]

My brother is x years old. I am 5 years older than him. Our combined age is 30 years old. How old is my brother Brother's age is x: I am 5 years older, meaning I'm x + 5: The combined age is found by adding: x + (x + 5) = 30 Group like terms: 2x + 5 = 30 To solve for x, [URL=' this equation into our search engine[/URL] and we get: x = [B]12.5[/B]

1/2 of the parent age is 34/2 = 17. 9 less than that is 17 - 9 = 8. The son is 8 years old. You can also write this as 1/2(34) - 9 --> 17 - 9 = 8.

n + 2n + 3n + 4n = 2 + 3 + 4 + 5 + 6 Solve for [I]n[/I] in the equation n + 2n + 3n + 4n = 2 + 3 + 4 + 5 + 6 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 2 + 3 + 4)n = 10n [SIZE=5][B]Step 2: Group the constant terms on the right hand side:[/B][/SIZE] 2 + 3 + 4 + 5 + 6 = 20 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 10n = + 20 [SIZE=5][B]Step 4: Divide each side of the equation by 10[/B][/SIZE] 10n/10 = 20/10 n = [B]2[/B]

n + 9n - 8 - 5 = 2n + 3 Solve for [I]n[/I] in the equation n + 9n - 8 - 5 = 2n + 3 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 9)n = 10n [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] -8 - 5 = -13 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 10n - 13 = 2n + 3 [SIZE=5][B]Step 4: Group variables:[/B][/SIZE] We need to group our variables 10n and 2n. To do that, we subtract 2n from both sides 10n - 13 - 2n = 2n + 3 - 2n [SIZE=5][B]Step 5: Cancel 2n on the right side:[/B][/SIZE] 8n - 13 = 3 [SIZE=5][B]Step 6: Group constants:[/B][/SIZE] We need to group our constants -13 and 3. To do that, we add 13 to both sides 8n - 13 + 13 = 3 + 13 [SIZE=5][B]Step 7: Cancel 13 on the left side:[/B][/SIZE] 8n = 16 [SIZE=5][B]Step 8: Divide each side of the equation by 8[/B][/SIZE] 8n/8 = 16/8 n = [B]2[/B]

n + 9n - 90 = 0 Solve for [I]n[/I] in the equation n + 9n - 90 = 0 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 9)n = 10n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 10n - 90 = [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -90 and 0. To do that, we add 90 to both sides 10n - 90 + 90 = 0 + 90 [SIZE=5][B]Step 4: Cancel 90 on the left side:[/B][/SIZE] 10n = 90 [SIZE=5][B]Step 5: Divide each side of the equation by 10[/B][/SIZE] 10n/10 = 90/10 n = [B]9[/B]

n - n = 10 - n Solve for [I]n[/I] in the equation n - n = 10 - n [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 - 1)n = 0n = 0 [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] = - n + 10 [SIZE=5][B]Step 3: Group variables:[/B][/SIZE] We need to group our variables and -n. To do that, we add n to both sides + n = -n + 10 + n [SIZE=5][B]Step 4: Cancel -n on the right side:[/B][/SIZE] n = [B]10[/B]

n = b + d^2a for a Let's start by isolating the one term with the a variable. Subtract b from each side: n - b = b - b + d^2a Cancel the b terms on the right side and we get: n - b = d^2a With the a term isolated, let's divide each side of the equation by d^2: (n - b)/d^2 = d^2a/d^2 Cancel the d^2 on the right side, and we'll display this with the variable to solve on the left side: a = [B](n - b)/d^2 [MEDIA=youtube]BCEVsZmoKoQ[/MEDIA][/B]

n increased by the difference between 10 times n and 9 Take this algebraic expression in pieces: [LIST] [*]10 times n: 10n [*]The difference between 10 times n and 9: 10n - 9 [*]n increased by the difference...: [B]n + (10n - 9)[/B] [/LIST]

n is equal to the product of 7 and the sum of m and 6 The sum of m and 6: m + 6 The product of 7 and this sum: 7(m + 6) We set this expression equal to n: [B]7(m + 6) = n[/B]

N squared multiplied by the difference of n and 3 n squared means we raise n to the power of 2: n^2 The difference of n and 3 means we subtract 3 from n: n - 3 Now we multiply both terms together: [B]n^2(n - 3)[/B]

n subtract m, multiply by c, then add w Take this algebraic expression in pieces: [LIST] [*]n subtract m: n - m [*]multiply by c: c(n - m) [*]Then add w: [B]c(n - m) + w[/B] [/LIST]

Free N-Grams Calculator - Takes a phrase and displays chracter unigrams, character bigrams, character trigrams, and character n-grams as well as word unigrams, word bigrams, word trigrams, and word n-grams. (ngrams)Also performs frequency analysis (number of instances of each letter)

n=i*x+y for i This is a literal equation. Subtract y from each side of the equation: n - y = i*x + y - y The y's cancel on the right side, so we have: n - y = ix Divide each side of the equation by x, to isolate i (n - y)/x = ix/x The x's cancel on the right side, so we have: i = [B](n - y)/x[/B]

Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and is spending $15 a week. [I]When will they both have the same amount of money in the bank?[/I] [I][/I] Set up the Account equation A(w) where w is the number of weeks that pass. Nancy (we add since savings means she accumulates [B]more[/B]): A(w) = 25w + 435 Shane (we subtract since spending means he loses [B]more[/B]): A(w) = 875 - 15w Set both A(w) equations equal to each other to since we want to see what w is when the account are equal: 25w + 435 = 875 - 15w [URL=' this equation into our search engine to solve for w[/URL] and we get: w =[B] 11[/B]

Free Natural Logarithm Table Calculator - Generates a natural logarithm table for the first (n) numbers rounded to (r) digits

Nava is 17 years older than Edward. the sum of Navas age and Edwards ages id 29. How old is Nava? Let Nava's age be n and Edward's age be e. We have 2 equations: [LIST=1] [*]n = e + 17 [*]n + e = 29 [/LIST] Substitute (1) into (2) (e + 17) + e = 29 Group like terms: 2e + 17 = 29 Running this equation [URL=' our search engine[/URL], we get: e = 6 Substitute this into equation (1) n = 6 + 17 [B]n = 23[/B]

Consider the recurrence relation T(n) =2 if n = 1, T(n?1) + 4n?2 if n > 1 (i) Derive the closed form expression f(n) for this recurrence relation. (ii) Prove that T(n) = f(n),?n ?N

Free Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability Index Calculator - Given a series of cash flows C_t at times t and a discount rate of (i), the calculator will determine the Net Present Value (NPV) at time 0, also known as the discounted cash flow model. Profitability Index Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator

Nia is trying to decide between two possible jobs. Job A pays $2000 a month with a 2% annual raise. Job B pays 24,000 a year with a $500 annual raise. Write a function to represent the annual salary for Job A after x years. Write a function to represent the annual salary for Job B after x years. After how many years would Nia have a greater salary at Job A? Nia Job A salary at time t: S(t) $2,000 per month equals $24,000 per year. So we have S(t) = 24,000(1.o2)^t Nia Job B salary at time t: S(t) $24,000 per year. So we have S(t) = 24,000 + 500t We want to know t when Job A salary is greater than Job B Salary: 24,000(1.o2)^t > 24,000 + 500t Time | A | B 0 | 24000 | 24000 1 | 24480 | 24500 2 | 24969.6 | 25000 3 | 25468.99 | 25500 4 | 25978.37 | 26000 5 | 26497.94 | 26500 6 | 27027.9 | 27000 7 | 27568.46 | 27500 8 | 28119.83 | 28000 9 | 28682.22 | 28500 10 | 29255.87 | 29000 11 | 29840.98 | 29500 12 | 30437.8 | 30000 13 | 31046.56 | 30500

Nick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that shows how much money Nick has after x amount of days. Set up the function M(x) where M(x) is the amount of money after x days. Since spending means a decrease, we subtract to get: [B]M(x) = 50 - 5x[/B]

Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 complete this equation to find his brothers age Let b be the brother's age and s be the sister's age. We're given two equations: [LIST=1] [*]s =4b [*]b + s = 20 [/LIST] Plug (1) into (2): b + 4b = 20 [URL=' this equation into the search engine[/URL], and we get: [B]b = 4[/B]

Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years? Let n be Nicole's age. Let d be Donald's age. We're given two equations: [LIST=1] [*]n = 0.5d [*]n + d = 72 [/LIST] Substitute equation (1) into (2): 0.5d + d = 72 1.5d = 72 [URL=' this equation into the search engine and solving for d[/URL], we get: d = [B]48[/B]

Nine times the sum of a number and 6 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The sum of a number and 6 means we add 6 to x: x + 6 9 times the sum: [B]9(x + 6)[/B]

nine times x is twice the sum of x and five Take this algebraic expression in 4 pieces: [U]Step 1: nine time x:[/U] 9x [U]Step 2: The sum of x and five means we add 5 to x:[/U] x + 5 [U]Step 3: The word [I]twice[/I] means we multiply the sum x + 5 by 2:[/U] 2(x + 5) [U]Step 4: The word [I]is[/I] means equal to, so we set 9x equal to 2(x + 5) to get our final algebraic expression of:[/U] [B]9x = 2(x + 5)[/B]

Free Normal Distribution Calculator - Calculates the probability that a random variable is less than or greater than a value or between 2 values using the Normal Distribution z-score (z value) method (Central Limit Theorem). Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability

Free Number Property Calculator - This calculator determines if an integer you entered has any of the following properties: * Even Numbers or Odd Numbers (Parity Function or even-odd numbers) * Evil Numbers or Odious Numbers * Perfect Numbers, Abundant Numbers, or Deficient Numbers * Triangular Numbers * Prime Numbers or Composite Numbers * Automorphic (Curious) * Undulating Numbers * Square Numbers * Cube Numbers * Palindrome Numbers * Repunit Numbers * Apocalyptic Power * Pentagonal * Tetrahedral (Pyramidal) * Narcissistic (Plus Perfect) * Catalan * Repunit

numerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the denominator the new fraction is 2/3. find the fraction. Let n be the numerator. Let d be the denominator. We're given 2 equations: [LIST=1] [*]n = d - 5 [*](n + 1)/(d + 1) = 2/3 [/LIST] Substitute equation (1) into equation (2) for n: (d - 5 + 1) / (d + 1) = 2/3 (d - 4) / (d + 1) = 2/3 Cross multiply: 3(d - 4) = 2(d + 1) To solve this equation for d, we type it in our search engine and we get: d = 14 Substitute d = 14 into equation (1) to solve for n: n = 14 - 5 n = 9 Therefore, our fraction n/d is: [B]9/14[/B]

n^2 - 1 = -99/100 Add 1 (100/100) to each side: n^2 - 1 + 1 = -99/100 + 100/100 Cancel the 1's on the left side: n^2 = 1/100 Take the square root of both sides: n = [B]1/10 or -1/10[/B]

n^2 = 64 Take the square root of each side: sqrt(n^2) = sqt(64) n = [B]8[/B]

n^2+n = odd Factor n^2+n: n(n + 1) We have one of two scenarios: [LIST=1] [*]If n is odd, then n + 1 is even. The product of an odd and even number is an even number [*]If n is even, then n + 1 is odd. The product of an even and odd number is an even number [/LIST]

n^2-n = even Factor n^2-n: n(n - 1) We have one of two scenarios: [LIST=1] [*]If n is odd, then n - 1 is even. The product of an odd and even number is an even number [*]If n is even, then n - 1 is odd. The product of an even and odd number is an even number [/LIST]

Oceanside Bike Rental Shop charges $15.00 plus $9.00 per hour for renting a bike. Dan paid $51.00 to rent a bike. How many hours was he hiking for? Set up the cost equation C(h) where h is the number of hours needed to rent the bike: C(h) = Cost per hour * h + rental charge Using our given numbers in the problem, we have: C(h) = 9h + 15 The problem asks for h, when C(h) = 51. 9h + 15 = 51 To solve for h, we [URL=' this equation into our search engine[/URL] and we get: h = [B]4[/B]

Oceanside Bike Rental Shop charges 16 dollars plus 6 dollars an hour for renting a bike. Mary paid 58 dollars to rent a bike. How many hours did she pay to have the bike checked out ? Set up the cost function C(h) where h is the number of hours you rent the bike: C(h) = Hourly rental cost * h + initial rental charge C(h) = 6h + 16 Now the problem asks for h when C(h) = 58, so we set C(h) = 58: 6h + 16 = 58 To solve this equation for h, we [URL=' it in our math engine[/URL] and we get: h = [B]7 hours[/B]

Of all smokers in particular district, 40% prefer brand A and 60% prefer brand B. Of those who prefer brand A, 30% are female, and of those who prefer brand B, 40% are female. Q: What is the probability that a randomly selected smoker prefers brand A, given that the person selected is a female? P(F) = P(F|A)*P(A) + P(F|B)*P(B) P(F) = 0.3*0.4 + 0.4*0.6 = 0.36 So, 36% of all the smokers are female. You are looking for P(A|F) P(A|F) = P(A and F)/P(F) P(A|F) = (P(F|A)*P(A))/P(F) P(A|F) = (0.3 * 0.4)/0.36 P(A|F) = [B]0.33 or 33%[/B]

Of the 20 boats at the Mariana, 10 were from Massachusetts. What is the probability that a randomly selected boat will be from Massachusetts? P(Boat from Massachusetts) = Number of Massachusetts boats / Total Boats at the Mariana P(Boat from Massachusetts) = 10/20 [URL=' this fraction, we get[/URL]: P(Boat from Massachusetts) = [B]1/2[/B]

Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend? Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (?2.71828), r is the interest rate expressed as a decimal, and t is the time in years. Round your answer to the nearest cent. [URL=' our continuous interest calculator[/URL], we get: A = [B]1,521.96[/B]

Oliver invests $1,000 at a fixed rate of 7% compounded monthly, when will his account reach $10,000? 7% monthly is: 0.07/12 = .00583 So we have: 1000(1 + .00583)^m = 10000 divide each side by 1000; (1.00583)^m = 10 Take the natural log of both sides; LN (1.00583)^m = LN(10) Use the identity for natural logs and exponents: m * LN (1.00583) = 2.30258509299 0.00252458479m = 2.30258509299 m = 912.064867899 Round up to [B]913 months[/B]

Omar mows lawns for $9.25 an hour. He spends $7.50 on gas for the mower. How much does he make if he works h hours? His revenue R(h) where h is the number of hours is denoted by: R(h) = Hourly Rate * h - Gas cost [B]R(h) = 9.25h - 7.50[/B]

On a particular road map, 1/2 inch represents 18 miles. About how many miles apart are 2 towns that are 2 1/2 inches apart on this map? A) 18 B) 22 1/2 C) 36 D) 45 E) 90 Set up a proportion of inches to miles where m is the number of miles for 2 1/2 inches. Note: 1/2 = 0.5 and 2 1/2 = 2.5 0.5/18 = 2.5/m [URL=' this proportion into the search engine[/URL], we get: [B]m = 90 Answer E[/B]

On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two grades was 138. Find the lowest grade. [U]Let h be the highest grade and l be the lowest grade. Set up the given equations:[/U] (1) h = l + 42 (2) h + l = 138 [U]Substitute (1) into (2)[/U] l + 42 + l = 138 [U]Combine l terms[/U] 2l + 42 = 138 [U]Enter that equation into our [URL=' calculator[/URL] to get[/U] [B]l = 48 [/B] [U]Substitute l = 48 into (1)[/U] h = 48 + 42 [B]h = 90[/B]

On your first draw, what is the probability of drawing a red card, without looking, from a shuffled deck containing 6 red cards, 6 blue cards, and 8 black cards? P(Red) = Total Red / Total Cards P(Red) = 6 red/(6 red + 6 blue + 8 black) P(Red) = 6/20 This fraction can be simplified. The [URL=' common factor of 6 and 20[/URL] is 2. So we divide top and bottom of our probability by 2: P(Red) = 6/2 / 20 / 2 P(Red) = [B]3/10[/B]

One number exceeds another by 15. The sum of the numbers is 51. What are these numbers? Let the first number be x, and the second number be y. We're given two equations: [LIST=1] [*]x = y + 15 [*]x + y = 51 [/LIST] Plug (1) into (2) (y + 15) + y = 51 Combine like terms: 2y + 15 = 51 [URL=' this equation into the search engine[/URL] and we get: [B]y = 18[/B] Now plug this into (1) to get: x = 18 + 15 [B]x = 33[/B]

One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a comma to separate your answers. Let the first number be x and the second number be y. We're given: [LIST=1] [*]x = 1/4y [*]x + y = 25 [/LIST] Substitute (1) into (2) 1/4y + y = 25 Since 1/4 = 0.25, we have: 0.25y + y = 25 [URL=' this equation into the search engine[/URL] to get: [B]y = 20 [/B] Now, substitute this into (1) to solve for x: x = 1/4y x = 1/4(20) [B]x = 5 [/B] The problem asks us to separate the answers by a comma. So we write this as: [B](x, y) = (5, 20)[/B]

One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers. Let the two numbers be x and y. We're given: [LIST=1] [*]x = 1/5y [*]x + y = 18 [/LIST] Substitute (1) into (2): 1/5y + y = 18 1/5 = 0.2, so we have: 1.2y = 18 [URL=' 1.2y = 18 into the search engine[/URL], and we get [B]y = 15[/B]. Which means from equation (1) that: x = 15/5 [B]x = 3 [/B] Our final answer is [B](x, y) = (3, 15)[/B]

One number is 3 times another. Their sum is 44. Let the first number be x, and the second number be y. We're given: [LIST=1] [*]x = 3y [*]x + y = 44 [/LIST] Substitute (1) into (2): 3y + y = 44 [URL=' this equation into the search engine[/URL], and we get: [B]y = 11[/B] Plug this into equation (1): x = 3(11) [B]x = 33[/B]

one number is 3 times as large as another. Their sum is 48. Find the numbers Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x = 3y [*]x + y = 48 [/LIST] Substitute equation (1) into equation (2): 3y + y = 48 To solve for y, [URL=' type this equation into the search engine[/URL] and we get: [B]y = 12[/B] Now, plug y = 12 into equation (1) to solve for x: x = 3(12) [B]x = 36[/B]

One number is 8 times another number. The numbers are both positive and have a difference of 70. Let the first number be x, the second number be y. We're given: [LIST=1] [*]x = 8y [*]x - y = 70 [/LIST] Substitute(1) into (2) 8y - y = 70 [URL=' this equation into our search engine[/URL], we get: [B]y = 10[/B] <-- This is the smaller number Plug this into Equation (1), we get: x = 8(10) [B]x = 80 [/B] <-- This is the larger number

one number is twice a second number. the sum of those numbers is 45. Let the first number be x and the second number be y. We're given: [LIST=1] [*]x = 2y [*]x + y = 45 [/LIST] Substitute Equation (1) into Equation (2): 2y + y = 45 [URL=' this equation into our search engine[/URL], we get: [B]y = 15[/B] Plug this into equation (1) to solve for x, and we get: x = 2(15) [B]x = 30[/B]

One positive number is one-fifth of another number. The difference between the two numbers is 192, find the numbers. Let the first number be x and the second number be y. We're given two equations: [LIST=1] [*]x = y/5 [*]x + y = 192 [/LIST] Substitute equation 1 into equation 2: y/5 + y = 192 Since 1 equals 5/5, we rewrite our equation like this: y/5 = 5y/5 = 192 We have fractions with like denominators, so we add the numerators: (1 + 5)y/5 = 192 6y/5 = 192 [URL=' this equation into our search engine[/URL], and we get: [B]y = 160[/B] Substitute this value into equation 1: x = 160/5 x = [B]32[/B]

The sum of 4 and p is written as: 4 + p We then take 1/3 of that, or multiply: 1/3(4 + p)

One thousand people in. room decide to shake hands with every other person in the room. Instead of one handshake per couple, each person must shake both of the hands of every person in the room with both his right and his left hand. (Tom will use his right hand to shake Dave's right hand and then Dave's left hand. Tom will then use his left hand to shake Dave's right hand and then Dave's left hand.) How many total handshakes will take place? 1000 people taken 2 at a time: [URL=' = 499,500 But each group of 2 makes 4 unique handshakes: 499,500 * 4 = [B]1,998,000[/B]

One-fourth the sum of m and p Take this algebraic expression in parts: [LIST] [*]The sum of m and p means we add p to m: m + p [*]1/4 of the sum mean we divide m + p by 4 [/LIST] [B](m + p)/4[/B]

One-half the sum of 5 and t The sum of 5 and t: 5 + t One-half of this means we multiply 5 + t by 1/2 [B](5 + t)/2[/B]

Free Opposite Numbers Calculator - Given a positive or negative integer (n), this calculates the opposite number of n

opposite of twice the quotient of a and a the quotient of a and a: a/a 1 Twice the quotient of a and a 2(1) 2 Opposite means multiply 2 by -1: -1 * 2 [B]-2[/B]

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Oscar makes a large purchase at Home Depot and plans to rent one of its trucks to take his supplies home. The most he wants to spend on the truck is $56.00. If Home Depot charges $17.00 for the first 75 minutes and $5.00 for each additional 15 min, for how long can Oscar keep the truck and remain within his budget? Set up the cost equation C(m) where m is the number of minutes for rental: C(m) = 17 * min(m, 75) + max(0, 5(m - 75)) If Oscar uses the first 75 minutes, he spends $17. So he's left with: $56 - $17 = $38 $38 / $5 = 7 Remainder 3 We remove the remainder 3, since it's not a full 15 minute block. So Oscar can rent the truck for: 7 * 15 minute blocks = [B]105 minutes[/B]

Out of 53 teachers 36 drink tea 18 drink coffee, 10 drink neither. how many drink both? Let T be tea drinkers Let C be coffee drinkers Let (T & C) be Tea & Coffee drinkers. And 53 are total. So we use the Union formula relation: C U T = C + T - (C & T) 53 = 18 + 36 - (C & T) C & T = 53 - (Not C & Not T) since we subtract people who don't drink coffee and don't drink tea C & T = 53 - 10 = 43 C U T = 18 + 36 - 43 C U T = [B]11[/B]

p(t)=6t represent the number of people p(t) that a number of turkeys can feed at Thanksgiving. How many people can 6 turkeys feed? Plug in t = 6 p(6) = 6(6) p(6) = 36

P(x)=25x-15,375 x=385 If x= 385, we have: P(385) = 25(385) - 15,375 P(385) = 9,625 - 15,375 P(385) = [B]-5,750[/B]

p(x)=2x-5 find the domain Using our[URL=' function calculator[/URL]: [B]All real numbers[/B]

p/q = f/q- f for f Isolate f in this literal equation. Factor out f on the right side: p/q = f(1/q - 1) Rewriting the term in parentheses, we get: p/q = f(1 - q)/q Cross multiply: f = pq/q(1 - q) Cancelling the q/q on the right side, we get: f = [B]p/(1 - q)[/B]

p/q=f/q-f for f To solve this literal equation for f, let's factor out f on the right side: p/q=f(1/q-1) Divide each side by (1/q - 1) p/(q(1/q - 1)) = f(1/q-1)/(1/q - 1) Cancelling the (1/q - 1) on the right side, we get: f = p/(1/q - 1) Rewriting this since (1/q -1) = (1 - q)/q since q/q = 1 we have: f = [B]pq/(1 - q)[/B]

Subtract 15 from each side: 5d/11 = P - 15 Multiply each side by 11 5d = 11p - 165 Divide each side of the equation by d: d = (11p - 165) ------------ 5

P=ab/c, for c Cross multiply: cP = ab Divide each side by P [B]c = (ab)/P[/B]

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Penelope and Owen work at a furniture store. Penelope is paid $215 per week plus 3.5% of her total sales in dollars, xx, which can be represented by g(x)=215+0.035x. Owen is paid $242 per week plus 2.5% of his total sales in dollars, xx, which can be represented by f(x)=242+0.025x. Determine the value of xx, in dollars, that will make their weekly pay the same. Set the pay functions of Owen and Penelope equal to each other: 215+0.035x = 242+0.025x Using our [URL=' calculator[/URL], we get: [B]x = 2700[/B]

Penny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% each year since. Let x = the number of years since 2010 and y = the value of the car. What will the value of the car be in 2020? Write the equation, using the variables above, that represents this situation and solve the problem, showing the calculation you did to get your solution. Round your answer to the nearest whole number. We have the equation y(x): y(x) = 25,000(0.97)^x <-- Since a 3 % decrease is the same as multiplying the starting value by 0.97 The problem asks for y(2020). So x = 2020 - 2010 = 10. y(10) = 25,000(0.97)^10 y(10) = 25,000(0.73742412689) y(10) = [B]18,435.60[/B]

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Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width? The perimeter P of a rectangle with length l and width w is: 2l + 2w = P We're given P = 372 and l = 99, so we have: 2(99) + 2w = 372 2w + 198 = 372 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 198 and 372. To do that, we subtract 198 from both sides 2w + 198 - 198 = 372 - 198 [SIZE=5][B]Step 2: Cancel 198 on the left side:[/B][/SIZE] 2w = 174 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2w/2 = 174/2 w = [B]87[/B]

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Free Phonetic Algorithms Calculator - Given a name, this calculator translates a name to one of the following 3 phonetic algorithms: * Soundex * Metaphone * New York State Identification and Intelligence System (NYSIIS)

Get a free pi coin. Use the link below: I am sending you 1?! Pi is a new digital currency developed by Stanford PhDs, with over 47 million members worldwide. To claim your Pi, follow this link [URL] and use my username (mathcelebrity) as your invitation code.--

Pleasantburg has a population growth model of P(t)=at^2+bt+P0 where P0 is the initial population. Suppose that the future population of Pleasantburg t years after January 1, 2012, is described by the quadratic model P(t)=0.7t^2+6t+15,000. In what month and year will the population reach 19,200? Set P(t) = 19,200 0.7t^2+6t+15,000 = 19,200 Subtract 19,200 from each side: 0.7t^2+6t+4200 = 0 The Quadratic has irrational roots. So I set up a table below to run through the values. At t = 74, we pass 19,200. Which means we add 74 years to 2012: 2012 + 74 = [B]2086[/B] t 0.7t^2 6t Add 15000 Total 1 0.7 6 15000 15006.7 2 2.8 12 15000 15014.8 3 6.3 18 15000 15024.3 4 11.2 24 15000 15035.2 5 17.5 30 15000 15047.5 6 25.2 36 15000 15061.2 7 34.3 42 15000 15076.3 8 44.8 48 15000 15092.8 9 56.7 54 15000 15110.7 10 70 60 15000 15130 11 84.7 66 15000 15150.7 12 100.8 72 15000 15172.8 13 118.3 78 15000 15196.3 14 137.2 84 15000 15221.2 15 157.5 90 15000 15247.5 16 179.2 96 15000 15275.2 17 202.3 102 15000 15304.3 18 226.8 108 15000 15334.8 19 252.7 114 15000 15366.7 20 280 120 15000 15400 21 308.7 126 15000 15434.7 22 338.8 132 15000 15470.8 23 370.3 138 15000 15508.3 24 403.2 144 15000 15547.2 25 437.5 150 15000 15587.5 26 473.2 156 15000 15629.2 27 510.3 162 15000 15672.3 28 548.8 168 15000 15716.8 29 588.7 174 15000 15762.7 30 630 180 15000 15810 31 672.7 186 15000 15858.7 32 716.8 192 15000 15908.8 33 762.3 198 15000 15960.3 34 809.2 204 15000 16013.2 35 857.5 210 15000 16067.5 36 907.2 216 15000 16123.2 37 958.3 222 15000 16180.3 38 1010.8 228 15000 16238.8 39 1064.7 234 15000 16298.7 40 1120 240 15000 16360 41 1176.7 246 15000 16422.7 42 1234.8 252 15000 16486.8 43 1294.3 258 15000 16552.3 44 1355.2 264 15000 16619.2 45 1417.5 270 15000 16687.5 46 1481.2 276 15000 16757.2 47 1546.3 282 15000 16828.3 48 1612.8 288 15000 16900.8 49 1680.7 294 15000 16974.7 50 1750 300 15000 17050 51 1820.7 306 15000 17126.7 52 1892.8 312 15000 17204.8 53 1966.3 318 15000 17284.3 54 2041.2 324 15000 17365.2 55 2117.5 330 15000 17447.5 56 2195.2 336 15000 17531.2 57 2274.3 342 15000 17616.3 58 2354.8 348 15000 17702.8 59 2436.7 354 15000 17790.7 60 2520 360 15000 17880 61 2604.7 366 15000 17970.7 62 2690.8 372 15000 18062.8 63 2778.3 378 15000 18156.3 64 2867.2 384 15000 18251.2 65 2957.5 390 15000 18347.5 66 3049.2 396 15000 18445.2 67 3142.3 402 15000 18544.3 68 3236.8 408 15000 18644.8 69 3332.7 414 15000 18746.7 70 3430 420 15000 18850 71 3528.7 426 15000 18954.7 72 3628.8 432 15000 19060.8 73 3730.3 438 15000 19168.3 74 3833.2 444 15000 19277.2

Time 1, distance apart is 105 + 85 = 190 So every hour, the distance between them is 190 * t where t is the number of hours. Set up our distance function: D(t) = 190t We want D(t) = 494 190t = 494 Divide each side by 190 [B]t = 2.6 hours[/B]

Figure 1, we have a cone, cylinder, and cube. Let's get the volume of each Cone volume = pir^2h/3 radius = s/2 h = s Cone Volume = pi(s/2)^2(s)/3 Cone Volume = pis^3/12 Volume of cube = s^3 Volume of cylinder = pir^2h Volume of cylinder = pi(s/2)^2s Volume of cylinder = pis^3/2 But Figure 2 has no sizes? For sides, height, etc. So I cannot answer the question until I have that.

Find the value of |A| if: (1) |P(A)| = 4 (2) |B| = |A|+ 1 and |AB| = 30 (3) |B| = |A|+ 2 and |P(B)|?|P(A)| = 24

(1), how can probability be greater than 1?

(1) |P(A)| = 4 <-- Cardinality of the power set is 4, which means we have 2^n = 4.[B] |A| = 2 [/B] (2) |B| = |A|+ 1 and |AB| = 30 |B| = 6 if [B]|A| = 5[/B] and |A x B| = 30 (3) |B| = |A|+ 2 and |P(B)|?|P(A)| = 24 Since |B| = |A|+ 2, we have: 2^(a + 2) - 2^a = 24 2^a(2^2 - 1) = 24 2^a(3) = 24 2^a = 8 [B]|A |= 3[/B] To check, we have |B| = |A| + 2 --> 3 + 2 = 5 So |P(B)| = 2^5 = 32 |P(A)| = 2^3 = 8 And 32 - 8 = 24

Find what was used: Used Money = Prepaid original cost - Remaining Credit Used Money = 20 - 17.47 Used Money = 2.53 Using (m) as the number of minutes, we have the following cost equation: C(m) = 0.11m C(m) = 2.53, so we have: 0.11m = 2.53 Divide each side by 0.11 [B]m = 23[/B]

Let x be the first number, y be the second number, and z be the number. We have the following equations: [LIST=1] [*]x + y + z = 305 [*]x = y - 5 [*]z = 3y [/LIST] Substitute (2) and (3) into (1) (y - 5) + y + (3y) = 305 Combine like terms: 5y - 5 = 305 Use our [URL=' solver[/URL] [B]y = 62 [/B] Substitute y = 62 into (3) z = 3(62) [B]z = 186 [/B] x = (62) - 5 [B]x = 57[/B]

A Web music store offers two versions of a popular song. The size of the standard version is 2.7 megabytes (MB). The size of the high-quality version is 4.7 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 4200 MB. How many downloads of the standard version were there?

A Web music store offers two versions of a popular song. The size of the standard version is 2.7 megabytes (MB). The size of the high-quality version is 4.7 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 4200 MB. How many downloads of the standard version were there? Let s be the standard version downloads and h be the high quality downloads. We have two equations: [LIST=1] [*]h = 3s [*]2.7s + 4.7h = 4200 [/LIST] Substitute (1) into (2) 2.7s + 4.7(3s) = 4200 2.7s + 14.1s = 4200 Combine like terms: 16.8s = 4200 Divide each side by 16.8 [B]s = 250[/B]

Plutonium 241 has a decay rate of 4.8 % per year. How many years will it take a 50 kg sample to decay to 10 kg? Since 4.8% is 0.048, we have decay as: 50 * (1 - 0.048)^n = 10 0.952^n = 0.2 Typing [URL=' into our math engine[/URL], we get: n = [B]32.7186 years[/B]

Free Poisson Distribution Calculator - Calculates the probability of 3 separate events that follow a poisson distribution.It calculates the probability of exactly k successes P(x = k)No more than k successes P (x <= k)Greater than k successes P(x >= k)Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis. Calculates moment number t using the moment generating function

Free Polar Conics Calculator - Given eccentricity (e), directrix (d), and angle θ, this determines the vertical and horizontal directrix polar equations.

Free Pool Volume Calculator - Given a round shaped pool, this calculates the volume (Capacity) in gallons of the pool when filled with water

Imagine you are in a game show. Prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and two are worth $10. You have to pay $20 to the host if your choice is not correct. Let the random variable x be the winning (a) What is your expected winning in this game? (b) Determine the standard deviation of x. (Round the answer to two decimal places) (a) 100(0.1) + 50(0.1) + 10(0.2) - 20 = 10 + 5 + 2 - 20 = [B]-3[/B] (b) 3.3 using our [URL=' deviation calculator[/URL]

Free Probability (A U B U C) Calculator - Calculates the probability of a union of a three event sample space, A, B, and C, as well as P(A), P(B), P(C), P(A ∩ B), P(A ∩ C), P(B ∩ C), P(A ∩ B ∩ C).

Free Probability (A U B) Calculator - Given a 2 event sample space A and B, this calculates the probability of the following events:P(A U B)P(A)P(B)P(A ∩ B)

Probability of getting 4 or 6 when rolling a dice P(4 or 6) = P(4) + P(6) P(4 or 6) = 1/6 + 1/6 P(4 or 6) = 2/6 We can simplify this. We [URL=' this fraction into our search engine, choose simplify[/URL], and we get: P(4 or 6) = [B]1/3[/B]

Sum of 8 equal to 5/36 shown [URL=' At least one 4 means one of three scenarios: [LIST=1] [*](4, not 4) = 1/6 * 5/6 = 5/36 [*](not 4, 4) = 5/6 * 1/6 = 5/36 [*](4, 4) = 1/6 * 1/6 = 1/36 [/LIST] The phrase "or", means we add both probabilities (sum of 8) and (at least one 4): 5/36 + (5/36 + 5/36 + 1/36) 16/36 Simplify by dividing each part of the fraction by 4 [B]4/9[/B]

product of 8 and the sum of 6 and 3y the sum of 6 and 3y 6 + 3y product of 8 and the sum of 6 and 3y [B]8(6 + 3y)[/B]

product of r plus 7 and 4 r plus 7 means we add 7 to r: r + 7 The product means we multiply the expression r + a 7 by 4: [B]4(r + 7)[/B]

product of x and y decreased by their sum Product of x and y: xy Their sum: x + y Product of x and y decreased by their sum: [B]xy - (x + y)[/B]

Free Profit Equation Calculator - Using the Profit Equation with inputs (Revenue-Cost-Profit-Tax), this determines the relevant output including gross proft, gross profit margin, net profit, and net profit margin.

Free Proportion Calculator - 1) Calculates the missing link of 2 equivalent proportions or ratios. 2) Also determines if two numerical proportions that you entered such as 1/10=6/12 are equivalent or not equivalent. Note: You can use all allowable operators such as =,<,≤,>,≥

Prove (p & !q) -> ~(p -> q) Truth Table p & !q p | q | p & !q F | F | F F | T | F T | F | T T | T | F Truth Table !(p -> q) p | q | !(p -> q) F | F | F F | T | F T | F | T T | T | F

Prove 0! = 1 Let n be a whole number, where n! represents the product of n and all integers below it through 1. The factorial formula for n is: n! = n · (n - 1) * (n - 2) * ... * 3 * 2 * 1 Written in partially expanded form, n! is: n! = n * (n - 1)! [U]Substitute n = 1 into this expression:[/U] n! = n * (n - 1)! 1! = 1 * (1 - 1)! 1! = 1 * (0)! For the expression to be true, 0! [U]must[/U] equal 1. Otherwise, 1! <> 1 which contradicts the equation above

[URL=' 0! = 1[/URL] Let n be a whole number, where n! represents: The product of n and all integers below it through 1. The factorial formula for n is n! = n (n - 1) (n - 2) ... 3 2 1 Written in partially expanded form, n! is: n! = n (n - 1)! [SIZE=5][B]Substitute n = 1 into this expression:[/B][/SIZE] n! = n (n - 1)! 1! = 1 (1 - 1)! 1! = 1 (0)! For the expression to be true, 0! [U]must[/U] equal 1. Otherwise, 1! ? 1 which contradicts the equation above [MEDIA=youtube]wDgRgfj1cIs[/MEDIA]

Prove P(A) = 1 - P(A) The sample space S contains an Event A and everything not A, called A' We know P(S) = 1 P(S) = P(A U A') P(A U A') = 1 P(A) + P(A') = 1 subtract P(A) from each side: P(A) = 1 - P(A) [MEDIA=youtube]dNLl_8vejyE[/MEDIA]

Use proof by contradiction. Assume sqrt(2) is rational. This means that sqrt(2) = p/q for some integers p and q, with q <>0. We assume p and q are in lowest terms. Square both side and we get: 2 = p^2/q^2 p^2 = 2q^2 This means p^2 must be an even number which means p is also even since the square of an odd number is odd. So we have p = 2k for some integer k. From this, it follows that: 2q^2 = p^2 = (2k)^2 = 4k^2 2q^2 = 4k^2 q^2 = 2k^2 q^2 is also even, therefore q must be even. So both p and q are even. This contradicts are assumption that p and q were in lowest terms. So sqrt(2) [B]cannot be rational. [MEDIA=youtube]tXoo9-8Ewq8[/MEDIA][/B]

Take an integer n. The next alternate consecutive integer is n + 2 Subtract the difference of the squares: (n + 2)^2 - n^2 n^2 + 4n + 4 - n^2 n^2 terms cancel, we get: 4n + 4 Factor out a 4: 4(n + 1) If n is odd, n + 1 is even. 4 * even is always even If n is even, n + 1 is odd. 4 * odd is always odd Since both cases are even, we've proven our statement. [MEDIA=youtube]J_E9lR5qFY0[/MEDIA]

Take two consecutive integers: n, n + 1 The difference of their cubes is: (n + 1)^3 - n^3 n^3 + 3n^2 + 3n + 1 - n^3 Cancel the n^3 3n^2 + 3n + 1 Factor out a 3 from the first 2 terms: 3(n^2 + n) + 1 The first two terms are always divisible by 3 but then the + 1 makes this expression not divisible by 3: 3(n^2 + n) + 1 = 1 (mod 3) [MEDIA=youtube]hFvJ3epqmyE[/MEDIA]

Take an integer n. The next consecutive integer is n + 1 Subtract the difference of the squares: (n + 1)^2 - n^2 n^2 + 2n + 1 - n^2 n^2 terms cancel, we get: 2n + 1 2 is even. For n, if we use an even: we have even * even = Even Add 1 we have Odd 2 is even. For n, if we use an odd: we have even * odd = Even Add 1 we have Odd Since both cases are odd, we've proven our statement. [MEDIA=youtube]RAi0HbH5bqc[/MEDIA]

Prove the following statement for non-zero integers a, b, c, If a divides b and b divides c, then a divides c. If an integer a divides an integer b, then we have: b = ax for some non-zero integer x If an integer b divides an integer c, then we have: c = by for some non-zero integer y Since b = ax, we substitute this into c = by for b: c = axy We can write this as: c = a(xy) [LIST] [*]Since x and y are integers, then xy is also an integer. [*]Therefore, c is the product of some integer multiplied by a [*]This means a divides c [/LIST] [MEDIA=youtube]VUIUFAFFVU4[/MEDIA]

Take two integers, r and s. We can write r as a/b for integers a and b since a rational number can be written as a quotient of integers We can write s as c/d for integers c and d since a rational number can be written as a quotient of integers Add r and s: r + s = a/b + c/d With a common denominator bd, we have: r + s = (ad + bc)/bd Because a, b, c, and d are integers, ad + bc is an integer since rational numbers are closed under addition and multiplication. Since b and d are non-zero integers, bd is a non-zero integer. Since we have the quotient of 2 integers, r + s is a rational number. [MEDIA=youtube]0ugZSICt_bQ[/MEDIA]

Take two arbitrary integers, x and y We can express the odd integer x as 2a + 1 for some integer a We can express the odd integer y as 2b + 1 for some integer b x + y = 2a + 1 + 2b + 1 x + y = 2a + 2b + 2 Factor out a 2: x + y = 2(a + b + 1) Since 2 times any integer even or odd is always even, then [B]x + y by definition is even[/B]. [MEDIA=youtube]9A-qe4yZXYw[/MEDIA]

Let us take an integer x which is both even [I]and[/I] odd. [LIST] [*]As an even integer, we write x in the form 2m for some integer m [*]As an odd integer, we write x in the form 2n + 1 for some integer n [/LIST] Since both the even and odd integers are the same number, we set them equal to each other 2m = 2n + 1 Subtract 2n from each side: 2m - 2n = 1 Factor out a 2 on the left side: 2(m - n) = 1 By definition of divisibility, this means that 2 divides 1. But we know that the only two numbers which divide 1 are 1 and -1. Therefore, our original assumption that x was both even and odd must be false. [MEDIA=youtube]SMM9ubEVcLE[/MEDIA]

Free Pyramids Calculator - Solves for Volume (Capacity), Surface Area, height, or radius of a Pyramid.

Free Pythagorean Theorem Trig Proofs Calculator - Shows the proof of 3 pythagorean theorem related identities using the angle θ:Sin²(θ) + Cos²(θ) = 1Tan²(θ) + 1 = Sec²(θ)Sin(θ)/Cos(θ) = Tan(θ)

q increased by the difference between 18 times q and 5 Take this algebraic expression in parts. 18 times q: 18q The difference between 18 times q and 5 means we subtract 5 from 18q: 18q - 5 q increased by the difference between 18 times q and 5 means we add 18q - 5 to q: q + (18q - 5) [B]q + 18q - 5[/B] IF we want to simplify, we group like terms: [B]19q - 5[/B]

q=c+d/5 for d Subtract c from each side to solve this literal equation: q - c = c - c + d/5 Cancel the c's on the right side, we get d/5 = q - c Multiply each side by 5: 5d/5 = 5(q - c) Cancel the 5's on the left side, we get: [B]d = 5(q - c)[/B]

Quadratic equation hacks using the discriminant Solve x^2- 4x+ 5 using a discriminant: Discriminant is: Discriminant = b^2- 4ac Discriminant = (-4)^2 - 4(1)(5) Discriminant = 16 - 20 Discriminant = -4 When Discriminant < 0, the quadratic has [I][U]no solution [MEDIA=youtube]RogZ3430_8E[/MEDIA][/U][/I]

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax² + bx + c = 0. Also generates practice problems as well as hints for each problem. * Solve using the quadratic formula and the discriminant Δ * Complete the Square for the Quadratic * Factor the Quadratic * Y-Intercept * Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)² + k * Concavity of the parabola formed by the quadratic * Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

Free Quadrilateral Calculator - Given 4 points entered, this determines the area using Brahmaguptas Formula and perimeter of the quadrilateral formed by the points as well as checking to see if the quadrilateral (quadrangle) is a parallelogram.

Free Quartic Equations Calculator - Solves quartic equations in the form ax⁴ + bx³ + cx² + dx + e using the following methods:1) Solve the long way for all roots and the discriminant Δ2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

quotient of the sum of 17 and x and y The sum of 17 and x means we add x to 17: 17 + x quotient of the sum of 17 and x and y means we divide 17 + x by y [B](17 + x)/y[/B]

quotient of the sum of 2 numbers and 6 The phrase [I]two numbers[/I] means we choose 2 arbitrary variables, let's call them x and y x, y The sum of 2 numbers: x + y quotient of the sum of 2 numbers and 6 [B](x + y)/6[/B]

quotient of the sum of 3 numbers and 3 The phrase [I]3 numbers[/I] means we choose 3 arbitrary variables: a, b,c The sum of the 3 numbers: a + b + c quotient of the sum of 3 numbers and 3 [B](a + b + c)/3[/B]

r varies directly with s and inversely with the square root of t Varies directly means we multiply Varies inversely means we divide There exists a constant k such that: [B]r = ks/sqrt(t)[/B]

Rachel borrowed 8000 at a rate of 10.5%, compounded monthly. Assuming she makes no payments, how much will she owe after 4 years? [U]Convert annual amounts to monthly[/U] 4 years = 12 * 4 = 48 months i = .105/12 = 0.00875 monthly [U]Build our accumulation function A(t) where t is the time in months[/U] A(48) = 8,000 * (1.00875)^48 A(48) = 8,000 * 1.5192 A(48) = [B]12,153.60 [/B] [URL=' can also use the balance calculator[/URL]

Rachel saved $200 and spends $25 each week. Roy just started saving $15 per week. At what week will they have the same amount? Let Rachel's account value R(w) where w is the number of weeks be: R(w) = 200 - 25w <-- We subtract -25w because she spends it every week, decreasing her balance. Let Roy's account value R(w) where w is the number of weeks be: R(w) = 15w Set them equal to each other: 200 - 25w = 15w To solve this equation, [URL=' type it into our search engine[/URL] and get: [B]w = 5[/B]

Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she sold 6 fewer books than she did on Tuesday. During the 3 days Rachel sold 19 books. Create an equation that can be used to find m, a number of books Rachel sold on Monday. Let me be the number of books Rachel sold on Monday. We're given Tuesday's book sales (t) and Wednesday's books sales (w) as: [LIST=1] [*]t = 2m [*]w = t - 6 [*]m + t + w = 19 [/LIST] Plug (1) and (2) into (3): Since t = 2m and w = t - 6 --> 2m - 6, we have: m + 2m + 2m - 6 = 19 Combine like terms: 5m - 6 = 19 [URL=' this equation into our search engine[/URL], we get: [B]m = 5[/B]

Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every copy of Math is Fun he sells. Let p represent his total pay (in dollars), and let c represent the number of copies of Math is Fun he sells. Write an equation relating to . Then use this equation to find his total pay if he sells 22 copies of Math is Fun. We want a sales function p where c is the number of copies of Math is Fun p = Price per sale * c + Base Salary [B]p = 40c + 1900 [/B] Now, we want to know Total pay if c = 22 p = 40(22) + 1900 p = 880 + 1900 p = [B]2780[/B]

raise 3 to the 4th power, subtract w from the result, then divide v by what you have Raise 3 to the 4th power: 3^4 Simplified, this is 81 Subtract w from the result. We subtract w from 81: 81 - w Then divide v by what you have. We divide v by (81 -w) [B]v/(81 - w)[/B]

raise 6 to the 4th power, add h to the result, then multiply what you have by 8 Raise 6 to the 4th power: 6^4 add h to the result: 6^4 + h Then multiply what we have by 8: [B]8(6^4 + h)[/B]

Raise 9 to the 3rd power, subtract d from the result, then divide what you have by c. This is an algebraic expression, let's take in parts (or chunks). Raise 9 to the 3rd power. This means we take 9, and raise it to an exponent of 3 9^3 Subtract d from the result, means we subtract d from 9^3 9^3 - d Now we divide 9^3 - d by c [B](9^3 - d) / c[/B]

raise c to the 2nd power, add the result to 8, then subtract what you have from d Raise c to the 2nd power: c^2 Add the result to 8: c^2 + 8 Subtract what you have from d: d - (c^2 + 8)

Raise c to the 7th power, divide the result by 4, then triple what you have. Take this algebraic expression in pieces. Raise c to the 7th power: c^7 Divide the result by 4, means we divide c^7 by 4 c^7 / 4 Triple what you have means multiply c^7 / 4 by 3 [B]3(c^7 / 4)[/B]

f to the 8th power: f^8 Multiply the result by g (f^8) * g

Raise f to the 8th power, divide the result by 5, then multiply 10 f to the 8th power means we raise f to the power of 8 using an exponent: f^8 Divide f^8 by 5 (f^8)/5 Now multiply this by 10: 10(f^8)/5 We can simplify this algebraic expression by dividing 10/5 to get 2 on top: 2[B](f^8)[/B]

Raise p to the 9th power, multiply the result by q, then divide what you have by r. Take this in steps: [LIST] [*]Raise p to the 9th power: p^9 [*]Multiply the result by q: qp^9 [*]Divide what you have (the result) by r: qp^9/r [/LIST] [B](qp^9)/r [MEDIA=youtube]I5PShTfas4Y[/MEDIA][/B]

raise q to the 5th power add the result to p then divide what you have by r Take this algebraic expression in parts: [LIST] [*]Raise q to the 5th power: q^5 [*]Add the result to p: p + q^5 [*]Divide what you have by r. This means we take our result above and divide it by r: [/LIST] [B](p + q^5)/r[/B]

raise the difference of 8 and v to the 7th power Difference of 8 and v 8 - v To the 7th power [B](8 - v)^7[/B]

Raise the difference of V and 7 to the 10th The difference of V and 7: V - 7 Raise this to the 10th power: [B](V - 7)^10[/B]

Raise the sum of k and j to the second power The sum of k and j is written as: k + j Raise the sum to the second power: [B](k + j)^2[/B]

Raise the sum of w and v to the 7 The sum of w and v: w + v Raise the sum to the 7: [B](w + v)^7[/B]

Free Random Number Generator Calculator - This program generates (n) random numbers between a set of values you specify. Example: Generate 5 random numbers between 0 and 100.

ratio of x cubed and the sum of y and 5 x cubed means we raise x to the power of 3: x^3 The sum of y and 5: y + 5 ratio of x cubed and the sum of y and 5 [B]x^3/(y + 5)[/B]

Free Rational Number Subtraction Calculator - Subtracting 2 numbers, this shows an equivalent operations is adding the additive inverse. p - q = p + (-q)

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will he be paid in the first 4 years? The formula for [U]interest[/U] using simple interest is: I = Prt where P = Principal, r = interest, and t = time. We're given P = 500, r =0.04, and t = 4. So we plug this in and get: I = 500(0.04)(4) I = [B]80[/B]

Rearrange the following equation to make x the subject, and select the correct rearrangement from the list below 3x + 2y 1 -------- = --- 4x + y 3 [LIST] [*]x = 7y/13 [*]x = 7y/5 [*]x = -7y [*]x = -3y [*]x = 3y/5 [*]x = -5y/13 [*]x = -y [/LIST] Cross multiply: 3(3x - 2y) = 4x + y Multiply the left side through 9x - 6y = 4x + y Subtract 4x from each side and add 6y to each side 5x = 7y Divide each side by 5 to isolate x, the subject of an equation is the variable to the left [B]x = 7y/5[/B]

rectangle abcd prove: triangle adc is congruent to triangle bcd 1. Given: ABCD is a rectangle 2. AB = CD since opposite sides of rectangle are congruent 3. BC = AD since opposite sides of rectangle are congruent 4. AC = AC by the Reflexive Property of Equality 5. triangle ADC = triangle CBA by the Side-Side-Side (SSS) Property

Free Rectangular Solid Calculator - Solves for Volume (Capacity) of rectangular solid Lateral Area of rectangular Solid Surface Area of rectangular solid.

Reece made a deposite into an account that earns 8% simple interest. After 8 years Reece has earned 400 dollars. How much was Reece's initial deposit? Simple interest formula: A = P(1 + it) where P is the amount of principal to be invested, i is the interest rate, t is the time, and A is the amount accumulated with interest. Plugging in our numbers, we get: 400 = P(1 + 0.08(8)) 400 = P(1 + 0.64) 400 = 1.64P 1.64P = 400 [URL=' this problem into our search engine[/URL], we get: P = [B]$243.90[/B]

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a ball at random. a. What is the probability that you choose a red or even numbered ball? b. What is the probability you choose a green ball or a ball numbered less than 5? a. The phrase [I]or[/I] in probability means add. But we need to subtract even reds so we don't double count: We have 18 total balls, so this is our denonminator for our fractions. Red and Even balls are {2, 4, 6, 8, 10, 12} Our probability is: P(Red or Even) = P(Red) + P(Even) - P(Red and Even) P(Red or Even) = 13/18 + 9/18 - 6/18 P(Red or Even) = 16/18 Using our [URL=' Simplify Calculator[/URL], we have: P(Red or Even) = [B]16/18[/B] [B][/B] b. The phrase [I]or[/I] in probability means add. But we need to subtract greens less than 5 so we don't double count: We have 18 total balls, so this is our denonminator for our fractions. Green and less than 5 does not exist, so we have no intersection Our probability is: P(Green or Less Than 5) = P(Green) + P(Less Than 5) - P(Green And Less Than 5) P(Green or Less Than 5) = 5/18 + 4/18 - 0 P(Green or Less Than 5) = 9/18 Using our [URL=' Simplify Calculator[/URL], we have: P(Red or Even) = [B]1/2[/B]

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Renee sells 6 gifts in 20 minutes. How many might she sell in 4 hrs What is 4 hours in minutes? 4 hours = 4 * 60 = 240 minutes. Now we are on a minutes to minutes basis, set up a proportion: 6/20 = x/240 where x is the number of gifts in 240 minutes (4 hours) Using our [URL=' calculator[/URL], we get: [B]x = 72[/B]

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate if 0.06 m per day. Which function can be used to find the thickness of the ice shelf in meters x days since the discovery? We want to build an function I(x) where x is the number of days since the ice shelf discovery. We start with 450 meters, and each day (x), the ice shelf loses 0.06m, which means we subtract this from 450. [B]I(x) = 450 - 0.06x[/B]

Reuben finished reading his book in x days. each day, he read 4 pages.His book has 28 pages. x (days) = Total Pages / Pages Per Day x = 28/4 [B]x = 7 days[/B]

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Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages. Let r be Richard's age. And a be Alvin's age. We have: [LIST=1] [*]r = 3a [*]a + r = 52 [/LIST] Substitute (1) into (2) a + 3a = 52 Group like terms: 4a = 52 [URL=' this into the search engine[/URL], we get [B]a = 13[/B]. This means Richard is 3(13) = [B]39[/B]

Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico? Let Rico's age be r Let Nico's age be n We're given two equations: [LIST=1] [*]r = n + 6 [*]n + r = 36 [/LIST] We plug equation (1) into equation (2) for r: n + n + 6 = 36 To solve this equation for n, we [URL=' it in our search engine[/URL] and we get: [B]n = 15[/B]

Rigby and Eleanor's combined score on the systems of equations test was 181. Rigby scored 9 more points than Eleanor. What were Eleanor and Rigby's scores? Let Rigby's score be r Let Eleanor's score be e We're given two equations: [LIST=1] [*]r = e + 9 [*]e + r = 181 [/LIST] Substitute equation (1) into equation (2): e + (e + 9) = 181 Group like terms: 2e + 9 = 181 To solve this equation for e, we [URL=' it in our search engine[/URL] and we get: e = [B]86[/B]

Robert buys 3 pounds of bananas at $0.50 per pound and 3 pounds of apples at $1.00 per pound. Which of the following expressions represents the total cost of the fruit he bought (in dollars)? Total Cost of Fruit = Bananas in pounds * cost per banana pound + Apples in pounds * cost per apple pound Total Cost of Fruit = 3($0.50) + 3($1.00) Total Cost of Fruit = $1.50 + $3.00 Total Cost of Fruit = [B]$4.00[/B]

Roberto has taken 17 photos photos are placed on each odd number page and the newspaper has 10 pages total. The pages with photographs will have 3 or 4 photos each. How many pages has 3 photos and how many pages have 4 photos? Odd pages are 1, 3, 5, 7, 9 17/5 = 3 with 2 remaining. So all 5 pages have 3 photos. Then with 2 left over, 2 pages get 4 photos. So 5 pages have [B]3 photos, and 2 pages have 2 photos[/B] 3(3) + 4(2) = 9 + 8 = 17

Roberto owns a trucking company. He charges $50 hook up fee and $2 per mile. How much to tow your car: 1mile , 2miles , 10miles ? The Cost Function C(m) where m is the number of miles is written as: C(m) = 2m + 50 The problem asks for C(1), C(2), and C(10) Calculate C(1) C(1) = 2(1) + 50 C(1) = 2 + 50 C(1) = [B]52[/B] Calculate C(2) C(2) = 2(2) + 50 C(2) = 4 + 50 C(2) = [B]54[/B] Calculate C(10) C(10) = 2(10) + 50 C(10) = 20 + 50 C(10) = [B]70[/B]

Rochelle deposits $4,000 in an IRA. What will be the value (in dollars) of her investment in 25 years if the investment is earning 8% per year and is compounded continuously? Using our [URL=' interest calculator[/URL], we get: [B]29,556.22[/B]

Use our [URL=' dice calculator[/URL], you have 2 ways to roll an 11 [LIST=1] [*](5, 6) --> P(5, 6) = 1/36 [*](6, 5)--> P(6, 5) = 1/36 [/LIST] [U]We want P(5, 6) + P(6, 5):[/U] P(5, 6) + P(6, 5) = 1/36 + 1/36 P(5, 6) + P(6, 5) = 2/36 P(5, 6) + P(6, 5) = [B]1/18[/B]

Ronnie, liza, vivien, and vina are classmates. They send each other a Valentines card. Find the number of Valentines cards they send altogether We've got 4 classmates. Which means each person sends 3 Valentine's cards (to everybody else in the class but themselves): 3 * 3 * 3 * 3 or 4 * 3 = 12 Valentine's cards.

Rosanne takes 190 milligrams of an antibiotic. Every hour, her body breaks down 50% of the drug. How much will be left after 5 hours Let the antibiotic amount be A(h) where h is the amount of hours after ingestion. We have: A(h) = 190 * (1 - 0.5)^h A(h) = 190 * (0.5)^h The problem asks for A(5): A(5) = 190 * (0.5)^5 A(5) = 190 * 0.03125 A(5) = [B]5.9375 milligrams[/B]

Rose weighs 140 pounds and gains 10%. What percent of her new weight must she lose to get back to 140 pounds? Find her new weight after the 10% gain: New Weight = Starting Weight * (1 + 10%) Since 10% is 0.1, we have: New Weight = Starting Weight * (1 + 0.1) New Weight = Starting Weight * (1.1) Plug in our numbers: New Weight = 140 * (1.1) New Weight = 154 To get back to 140, Rose must lose 154 - 140 = 14 pounds. As a percentage of her new weight, [URL=' type 14/154 into our search engine[/URL], and get: [B]9.09% [/B] [I]We read this as, Rose must lose 9.09% of her current body weight of 154 pounds to get back to her starting weight of 140 pounds.[/I]

Roster form of: A = {3x-2/x are integers between 0 and 8} x = 0 = Undefined since we divide by 0 x = 1: 3*1 + 2/1 = 5 x = 2: 3*2 + 2/2 = 7 x = 3: 3*3 + 2/3 = 9.66666666666667 x = 4: 3*4 + 2/4 = 12.5 x = 5: 3*5 + 2/5 = 15.4 x = 6: 3*6 + 2/6 = 18.3333333333333 x = 7: 3*7 + 2/7 = 21.2857142857143 x = 8: 3*8 + 2/8 = 24.25 [B]A = {(0, undefined), (1, 5), (2, 7), (3, 9.6667), (4, 12.5), (5, 15.4), (6, 18.3333), (7, 21.2857142857143), (8, 24.25)}[/B]

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rs+h^2=1 for h Subtract rs from each side to isolate h: rs - rs + h^2 = 1 - rs Cancel the rs on the left side: h^2 = 1 - rs Take the square root of each side: sqrt(h^2) = sqrt(1 - rs) [B]h = +- sqrt(1 -rs)[/B]

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s = tu^2 for u Divide each side by t u^2 = s/t Take the square root of each side [LIST] [*]u = sqrt(s/t) [*]u = -sqrt(s/t) [/LIST] We have two answers due to negative number squared is positive

S equals the quotient of r and the sum of r and 8. A quotient means a fraction, so we have: [B]S = r/(r + 8)[/B]

Sadie and Connor both play soccer. Connor scored 2 times as many goals as Sadie. Together they scored 9 goals. Could Sadie have scored 4 goals? Why or why not? [U]Assumptions:[/U] [LIST] [*]Let Connor's goals be c [*]Let Sadie's goals be s [/LIST] We're given the following simultaneous equations: [LIST=1] [*]c = 2s [*]c + s = 9 [/LIST] We substitute equation (1) into equation (2) for c: 2s + s = 9 To solve the equation for s, we type it in our search equation and we get: s = [B]3[/B] So [U][B]no[/B][/U], Sadie could not have scored 4 goals since s = 3

sales 45,000 commission rate is 3.6% and salary is $275 Set up the commission function C(s) where s is the salary: C(s) = Commission * s + salary We're given: C(s) = 45,000, commission = 3.6%, which is 0.036 and salary = 275, so we have: 0.036s + 275 = 45000 To solve for s, we type this equation into our search engine and we get: s = [B]1,242,361.11[/B]

Sally and Adam works a different job. Sally makes $5 per hour and Adam makes $4 per hour. They each earn the same amount per week but Adam works 2 more hours. How many hours a week does Adam work? [LIST] [*]Let [I]s[/I] be the number of hours Sally works every week. [*]Let [I]a[/I] be the number of hours Adam works every week. [*]We are given: a = s + 2 [/LIST] Sally's weekly earnings: 5s Adam's weekly earnings: 4a Since they both earn the same amount each week, we set Sally's earnings equal to Adam's earnings: 5s = 4a But remember, we're given a = s + 2, so we substitute this into Adam's earnings: 5s = 4(s + 2) Multiply through on the right side: 5s = 4s + 8 <-- [URL=' 4(s + 2)[/URL] [URL=' this equation into the search engine[/URL], we get s = 8. The problem asks for Adam's earnings (a). We plug s = 8 into Adam's weekly hours: a = s + 2 a = 8 + 2 [B]a = 10[/B]

Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64. Let Sally's age be s. Let Mark's age be m. We're given two equations: [LIST=1] [*]s = m + 4 [*]2s + 5m = 64 <-- [I]Since Twice means we multiply by 2[/I] [/LIST] Substitute equation (1) into equation (2): 2(m + 4) + 5m = 64 Multiply through: 2m + 8 + 5m = 64 Group like terms: (2 + 5)m + 8 = 64 7m + 8 = 64 [URL=' this equation into the search engine[/URL] and we get: m = [B]8[/B]

Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy's age, j, if he is the younger man. Let Sam's age be s. Let' Jeremy's age be j. We're given: [LIST=1] [*]s = j + 2 <-- consecutive odd integers [*]sj = 783 [/LIST] Substitute (1) into (2): (j + 2)j = 783 j^2 + 2j = 783 Subtract 783 from each side: j^2 + 2j - 783 = 0 <-- This is the equation to find Jeremy's age. To solve this, [URL=' type this quadratic equation into the search engine[/URL] and get: j = 27, j = -29. Since ages cannot be negative, we have: [B]j = 27[/B]

Sam bought 8 new basketball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 40 cards left. How many cards did Sam start with? Let the starting about of cards be s. Sam adds 8 new cards, so he has s + 8. Then the dog ate half, so he's left with half. Sam is left with 40 cards: (s + 8)/2 = 40 Cross multiply: s + 8 = 80 [URL=' s + 8 = 80 into the search engine[/URL], and we get [B]s = 72[/B]

Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John Let John's age be j. We're given the following equation: 3j - 20 = 52 ([I]Less than[/I] means we subtract) To solve for j, we [URL=' this equation into our search engine[/URL] and we get: j = [B]24[/B]

Sam purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c that Sam paid. Cost Function is: [B]c = 4n[/B] Or, using n as a function variable, we write: c(n) = 4n

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Sara has a box of candies. In the box there are 8 pink candies, 7 purple candies and 5 blue candies. She takes one candy and records its color. She then puts it back in the box and draws another candy. What is the probability of taking out a pink candy followed by a blue candy? [B][U]Calculate the total number of candies:[/U][/B] Total candies = Pink + Purple + Blue Total candies = 8 + 7 + 5 Total candies = 20 [B][U]Calculate the probability of drawing one pink candy:[/U][/B] P(Pink) = 8/20 Using our [URL=' reduction calculator[/URL], we get: P(Pink) = 2/5 [B][U]Calculate the probability of drawing one blue candy:[/U][/B] P(Blue) = 5/20 <-- [I]20 options since Sara replaced her first draw[/I] Using our [URL=' reduction calculator[/URL], we get: P(Blue) = 1/4 The problem asks for the probability of a Pink followed by a Blue. Since each event is independent, we multiply: P(Pink, Blue) = P(Pink) * P(Blue) P(Pink, Blue) = 2/5 * 1/4 P(Pink, Blue) = 2/20 Using our [URL=' reduction calculator[/URL], we get: P(Pink, Blue) = [B]1/10 or 10%[/B]

Sara opened an account with $800 and withdrew $20 per week. Jordan opened an account with $500 and deposited $30 per week. In how many weeks will their account be equal? Each week, Sara's account value is: 800 - 20w <-- Subtract because Sara withdraws money each week Each week, Jordan's account value is: 500 + 30w <-- Add because Jordan deposits money each week Set them equal to each other: 800 - 20w = 500 + 30w Using our [URL=' solver[/URL], we get w = 6. Check our work: 800 - 20(6) 800 - 120 680 500 + 30(6) 500 + 180 680

Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money from her account and still have money left? Let w be the number of weeks. We have the following equation for the Balance after w weeks: B(w) = 250 - 25w [I]we subtract for withdrawals[/I] The ability to withdrawal money means have a positive or zero balance after withdrawal. So we set up the inequality below: 250 - 25w >= 0 To solve this inequality for w, we [URL=' it in our search engine[/URL] and we get: w <= [B]10 So Sarah can withdrawal for up to 10 weeks[/B]

Sarah makes $9 per hour working at a daycare center and $12 per hour working at a restaurant. Next week, Sarah is scheduled to work 8 hours at the daycare center. Which of the following inequalities represents the number of hours (h) that Sandra needs to work at the restaurant next week to earn at least $156 from these two jobs? Set up Sarah's earnings function E(h) where h is the hours Sarah must work at the restaurant: 12h + 9(8) >= 156 <-- The phrase [I]at least[/I] means greater than or equal to, so we set this up as an inequality. Also, the daycare earnings are $9 per hour * 8 hours Multiplying through and simplifying, we get: 12h + 72 >= 156 We [URL=' this inequality into the search engine[/URL], and we get: [B]h>=7[/B]

Sarah rolls 2 fair dice and adds the results from each. Work out the probability of getting a total that is a factor of 6. Factors of 6 are {6, 12} [URL='(Roll a 6)[/URL] = 5/36 [URL='(Roll a 12)[/URL] = 1/36 P(Roll a 6 or Roll a 12) = P(Roll a 6) + P(Roll a 12) P(Roll a 6 or Roll a 12) = 5/36 + 1/36 P(Roll a 6 or Roll a 12) = 6/36 Using our [URL=' simplifier[/URL], we see that: P(Roll a 6 or Roll a 12) = [B]1/6[/B]

Sarah sells cookies. She has a base month salary of $500 and makes $50 for every cookie she sells. whats is the equation. Let S(c) be the equation for the money Sarah makes selling (c) cookies. We have: S(c) = Cost per cookies * c cookies + Base Salary [B]S(c) = 50c + 500[/B]

This is a practice exam for the SAT (Standard Aptitude Test).

Savannah is a salesperson who sells computers at an electronics store. She makes a base pay of $90 each day and is also paid a commission for each sale she makes. One day, Savannah sold 4 computers and was paid a total of $100. Write an equation for the function P(x), representing Savannah's total pay on a day on which she sells x computers. If base pay is $90 per day, then the total commission Savannah made for selling 4 computers is: Commission = Total Pay - Base Pay Commission = 100 - 90 Commission = $10 Assuming the commission for each computer is equal, we need to find the commission per computer: Commission per computer = Total Commission / Number of Computers Sold Commission per computer = 10/4 Commission per computer = $2.50 Now, we build the Total pay function P(x): Total Pay = Base Pay + Commission * Number of Computers sold [B]P(x) = 90 + 2.5x[/B]

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Scientists are studying a cell that divides in half every 15 minutes. How many cells will there by after 2.5 hours? Divide 2.5 hours into 15 minute blocks. 2.5 hours = 2(60) + 0.5(60) minutes 2.5 hours = 120 + 30 minutes 2.5 hours = 150 minutes Now determine the amount of 15 minute blocks 150 minutes/15 minutes = 10 blocks or divisions [LIST] [*]We start with 1 cell at time 0, and double it every 15 minutes [*]We have A(0) = 1, we want A(10). [*]Our accumulation function is A(t) = A(0) * 2^t [/LIST] A(10) = 1 * 2^10 A(10) = [B]1024[/B]

If a business sells for $1,000,000 (hypothetically)and the proceeds are paid out over 5 years, using the following breakdown: 10% in the first year 15% in the second year 25% in years 3 through 5 Calculate the payouts: [LIST] [*]Year 1: 10% * $1,000,000 = $100,000 [*]Year 2: 15% * $1,000,000 = $150,000 [*]Year 3: 25% * $1,000,000 = $250,000 [*]Year 4: 25% * $1,000,000 = $250,000 [*]Year 5: 25% * $1,000,000 = $250,000 [/LIST] To check our work, add up our proceed payouts: $100,000 + $150,000 + $250,000 + $250,000 + $250,000 = $1,000,000

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Sergeant U has 360 rounds of ammunition to distribute to Lance Corporal (LCpl) F, Lance Corporal (LCpl) M and Lance Corporal (LCpl) Z in the ratio 3:5:7. How many rounds did Lance Corporal (LCpl) M receive? Our ratio denominator is: 3 + 5 + 7 = 15 Lance Corporal (LCpl) M gets 5:15 of the ammunition. [URL=' our fraction simplifier[/URL], we see that 5/15 = 1/3 So we take 360 rounds of ammunition times 1/3: 360/3 = [B]120[/B]

Serial numbers for a product are to be using 3 letters followed by 4 digits. The letters are to be taken from the first 8 letters of the alphabet with no repeats. The digits are taken from numbers 0-9 with no repeats. How many serial numbers can be generated The serial number is organized with letters (L) and digits (D) like this: LLLDDDD Here's how we get the serial number: [LIST=1] [*]The first letter can be any of 8 letters A-H [*]The second letter can be any 7 of 8 letters A-H [*]The third letter can be any 6 of 8 letters A-H [*]The fourth digit can be any of 10 digits 0-9 [*]The fifth digit can be any 9 of 10 digits 0-9 [*]The sixth digit can be any 8 of 10 digits 0-9 [*]The seventh digit can be any 7 of 10 digits 0-9 [/LIST] We multiply all possibilities: 8 * 7 * 6 * 10 * 9 * 8 * 7 [B]1,693,440[/B]

Free Set Notation Calculator - Given two number sets A and B, this determines the following: * Union of A and B, denoted A U B * Intersection of A and B, denoted A ∩ B * Elements in A not in B, denoted A - B * Elements in B not in A, denoted B - A * Symmetric Difference A Δ B * The Concatenation A · B * The Cartesian Product A x B * Cardinality of A = |A| * Cardinality of B = |B| * Jaccard Index J(A,B) * Jaccard Distance J_σ(A,B) * Dice's Coefficient * If A is a subset of B * If B is a subset of A

Seth is constantly forgetting the combination to his lock. He has a lock with four dials. (Each has 10 numbers 0-9). If Seth can try one lock combination per second, how many seconds will it take him to try every possible lock combination? Start with 0001, 0002, all the way to 9999 [URL=' you do this[/URL], you get 10,000 combinations. One per second = 10,000 seconds

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself how many plums did she have at first? Let p be the number of plums Shalini started with. We have: [LIST] [*]0.4 given to her brother [*]20% which is 0.2 given away to her sister [*]What this means is she kept 1 - (0.4 + 0.2) = 1 - 0.6 = 0.4 for herself [/LIST] 0.4p = 16 Divide each side by 0.4 [B]p = 40[/B]

Shanti had 275 red beads and 3 tines as many blue beads as red beads. She used a total of 156 beads to make a bracelet how many beads did she have left? Calculate Blue Beads: Blue Beads =3 * Red Beads Blue Beads = 3(275) Blue Beads = 825 Subtract off the beads Shanti used for the bracelet: 825 - 156 = [B]669[/B]

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked both jobs for a total of 30 hours, and a total of $690. How long did Giselle work as a carpenter and how long did she work as a blacksmith? Assumptions: [LIST] [*]Let b be the number of hours Giselle worked as a blacksmith [*]Let c be the number of hours Giselle worked as a carpenter [/LIST] Givens: [LIST=1] [*]b + c = 30 [*]25b + 20c = 690 [/LIST] Rearrange equation (1) to solve for b by subtracting c from each side: [LIST=1] [*]b = 30 - c [*]25b + 20c = 690 [/LIST] Substitute equation (1) into equation (2) for b 25(30 - c) + 20c = 690 Multiply through: 750 - 25c + 20c = 690 To solve for c, we [URL=' this equation into our search engine[/URL] and we get: c = [B]12 [/B] Now, we plug in c = 12 into modified equation (1) to solve for b: b = 30 - 12 b = [B]18[/B]

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants it to be 5 times as long as it is wide. What dimensions should the play area be? Sheila wants: [LIST=1] [*]l =5w [*]2l + 2w = 100 <-- Perimeter [/LIST] Substitute (1) into (2) 2(5w) + 2w = 100 10w + 2w = 100 12w = 100 Divide each side by 12 [B]w = 8.3333[/B] Which means l = 5(8.3333) -->[B] l = 41.6667[/B]

Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry? Let Sherry's age be s. Let the mom's age be m. We're given two equations: [LIST=1] [*]s = m - 31 [*]m + s = 61 [/LIST] Substitute equation (1) into equation (2) for s: m + m - 31 = 61 To solve for m, [URL=' type this equation into our search engine[/URL] and we get: m = 46 Now, we plug m = 46 into equation (1) to find Sherry's age s: s = 46 - 31 s = [B]15[/B]

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To do this, we need rationalize the denominator. This means get rid of the radical: Multiply top and bottom by sqrt(5) 2sqrt(5)/sqrt(5) * sqrt(5) sqrt(5) * sqrt(5) = sqrt(25) so we have: 2sqrt(5)/sqrt(25) sqrt(25) = 5, so we have: [B]2sqrt(5)/5[/B] [MEDIA=youtube]jearVN9LhBE[/MEDIA]

[SIZE=4]We know that 2^3 = 8, so we can rewrite this as: 2^4 x (2^3)^7 (2^3)^7 = 2^3 * 7 = 2^21 2^4 x 2^21 2^(4 + 21) [B]2^25[/B] [B][/B] [B][MEDIA=youtube]HWMQoH8Pl7U[/MEDIA][/B][/SIZE]

Simplify the monomial in parentheses: 2^3x^2*3y^3 8x^6y^3 Now we update the multiplication: 6x^2y^3(8x^6y^3) 6*8 x^(2 + 6)y^(3 + 3) [B]48x^8y^6[/B] [MEDIA=youtube]rmuDx027gL4[/MEDIA]

7sqrt(3) is broken down. sqrt(12) is not broken down. Let's find all the factors of 12 and see if we stumble on a perfect square: [LIST] [*]1 * 12 [*]2 * 6 [*]3 * 4 [/LIST] 4 is a perfect square, since sqrt(4) = 2. So sqrt(12) = sqrt(3 * 4) We pull the sqrt(4) = 2 outside the radical and rewrite our problem as: 7sqrt(3) - 2sqrt(3) These are like terms, so we have: (7 - 2)sqrt(3) [B]5sqrt(3) [/B] [MEDIA=youtube]ljXVXWnKiWY[/MEDIA]

Answer Choices [LIST] [*]A) log(3) [*]B) log(48) [*]C) 16 [*]D) log(8) [*]E) log(16) [/LIST] We know that log(ab) = log(a) = log(b) Looking at our problem, we see that a = 4 and b = 12, so we have: log(4) + log(12) = log(4 * 12) log(4) + log(12) = [B]log(48) Answer B[/B] [B] [MEDIA=youtube]vJr8lcbK-EE[/MEDIA][/B]

We know the following: [LIST] [*]csc(x) = 1/sin(x) [*]sec(x) = 1/cos(x) [*]cot(x) = 1/tan(x) [/LIST] We can rewrite our original expression as: sin(x) * cos(x) * tan(x)/sin(x) * cos(x) * tan(x) Everything cancels and we are left with [B]1[/B] [MEDIA=youtube]MsL-Ni4Hen4[/MEDIA]

We know from the pythagorean theorem: [SIZE=5][B]sin^2(x) + cos^2(x) = 1[/B] [B]Subtract sin^2(x) from each side and we get:[/B] [B][B]cos^2(x) = 1 - [B]sin^2(x)[/B][/B][/B] [B][B][B]We can rewrite our original expression as:[/B][/B][/B] [B][B][B]sin^2(x)/cos^2(x)[/B][/B][/B] [/SIZE] [B][B][B][SIZE=5]But this expression [/SIZE][SIZE=4]equals[/SIZE][SIZE=5] tan^2(x)[/SIZE][/B][/B][/B] [MEDIA=youtube]zqYg0VRq5Ak[/MEDIA]

Free Simultaneous Equations Calculator - Solves a system of simultaneous equations with 2 unknowns using the following 3 methods:1) Substitution Method (Direct Substitution)2) Elimination Method3) Cramers Method or Cramers Rule Pick any 3 of the methods to solve the systems of equations 2 equations 2 unknowns

sin(x)cot(x) We know that cot(x) = cos(x)/sin(x), so we rewrite this as: sin(x)cos(x)/sin(x) The sin(x) terms cancel and we get: [B]cos(x)[/B]

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Six Years ago, 12.2% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then. (a) Which of the following is the hypothesis to be conducted? A. H0: p = 0.122, H1 p > 0.122 B. H0: p = 0.122, H1 p <> 0.122 C. H0: p = 0.122, H1 p < 0.122 (b) Which of the following is a Type I error? A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. c) Which of the following is a Type II error? A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% (a) [B]C H0: p = 0.122, H1: p < 0.122[/B] because a null hypothesis should take the opposite of what is being assumed. So the assumption is that nothing has changed while the hypothesis is that the rate has decreased. (b) [B]C.[/B] The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. Type I Error is rejecting the null hypothesis when it is true c) [B]C.[/B] The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% Type II Error is accepting the null hypothesis when it is false.

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point. Calculate the revenue function R(c) where s is the number of sodas sold: R(s) = Sale Price * number of units sold R(s) = 50s Calculate the cost function C(s) where s is the number of sodas sold: C(s) = Variable Cost * s + Fixed Cost C(s) = 0.25s + 900 Our break-even point is found by setting R(s) = C(s): 0.25s + 900 = 50s We [URL=' this equation into our search engine[/URL] and we get: s = [B]18.09[/B]

Solve 11 - 1/2y = 3 + 6x for y Subtract 11 from each side so we can isolate the y term: 11 -11 - 1/2y = 3 + 6x - 11 Cancelling the 11's on the left side, we get: -1/2y = 6x - 8 <-- Since 3 - 11 = -8 Multiply both sides of the equation by -2 to remove the -1/2 on the left side: -2(-1/2)y = -2(6x - 8) Simplifying, we get: y = [B]-12x + 16 [MEDIA=youtube]38uwIaj88Lw[/MEDIA][/B]

Solve a= (a + b + c + d)/4 for c Cross multiply: 4a = a + b + c + d Subtract a + b+ d from each side to isolate c: 4a - a - b - d = a + b + c + d - a - b - d Canceling the a, b, and d from the right side, we get: c = [B]3a - b - d [/B]

Solve for h. rs + h^2 = l [U]Subtract rs from each side to isolate h:[/U] rs - rs + h^2 = l - rs [U]Cancel the rs terms on the left side, and we get:[/U] h^2 = l - rs [U]Take the square root of each side:[/U] h = [B]sqrt(l - rs)[/B]

1/3x + 1/2 = 2(3/4x - 5)

Solve mgh=1/2mv^2+1/2(2/5)mr^2(v^2/r^2) for v 1/2(2/5) = 1/5 since the 2's cancel r^2/r^2 = 1 So we simplify, and get: mgh=1/2mv^2+1/5(mv^2) for v Divide each side by m, so m's cancel in each term on the left and right side: gh = 1/2v^2 + 1/5(v^2) Combine like terms for v^2 on the right side: 1/2 + 1/5 = 7/10 from our [URL=' calculator[/URL] So we have: gh = 7v^2/10 Multiply each side by 10: 10gh = 7v^2 Now divide each side by 7 10gh/7 = v^2 Take the square root of each side: [B]v = sqrt(10gh/7)[/B]

Hello everyone. I am stuck on a work question that we are required to solve using the matrix (or Gauss-Jordan) method. [CENTER]"A car rental company wants to buy 100 new cars. Compact cars cost $12,000 each, intermediate size cars cost $18,000 each, full size cars cost $24,000 each, and the company has a budget of $1,500,000. If they purchase twice as many compact cars as intermediate sized cars, determine the number of cars of each type that they buy, assuming they spend the entire budget." [/CENTER] I am fairly certain that I could solve this easily, except I cannot figure out the proper three equations that correspond to this question. I someone could help me figure them out, it would be greatly appreciated!

Some hot dogs come in packages of 8. Why would a baker of hot dog buns package 7 hot dog buns to a package For customers that like to have matching hot dogs and buns, consider this scenario. For the first round, you have one extra hot dog. Now you buy a hot dog buns package. You're over 6 buns. This continues... We want to see when packaging and hot dogs math. Find the least common multiple of 7 and 8 so that packages match. [URL='(7, 8[/URL][I][URL=') [/URL]= 56[/I]

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large redwood tree was, the ranger said that he wouldn't tell its height, but would give Sonia a clue. How tall is the redwood tree Sonia asked about? Sonia said the tree is 64 times my height. The tree is also 112 feet taller than the tree next to it. The two trees plus my height total 597.5 feet. [LIST] [*]Rangers's height = n [*]Tree height = 64n [*]Smaller tree height = 64n - 112 [*]Total height = 64n - 112 + 64n = 597.5 [/LIST] Solve for [I]n[/I] in the equation 64n - 112 + 64n = 597.5 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (64 + 64)n = 128n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 128n - 112 = + 597.5 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -112 and 597.5. To do that, we add 112 to both sides 128n - 112 + 112 = 597.5 + 112 [SIZE=5][B]Step 4: Cancel 112 on the left side:[/B][/SIZE] 128n = 709.5 [SIZE=5][B]Step 5: Divide each side of the equation by 128[/B][/SIZE] 128n/128 = 709.5/128 n = 5.54296875 Tree height = 64 * ranger height Tree height = 64 * 5.54296875 Tree height = [B]354.75 feet[/B]

Sound travels about 340 m/s. The function d(t) = 340t give the distance d(t),in meters., that sound travel in T seconds. How far goes sound traveling 59s? What we want is d(59) d(59) = 340m/s(59s) = [B]20,060m[/B]

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Sports radio stations numbered 220 in 1996. The number of sports radio stations has since increased by approximately 14.3% per year. Write an equation for the number of sports radio stations for t years after 1996. If the trend continues, predict the number of sports radio stations in 2015. Equation - where t is the number of years after 1996: R(t) = 220(1.143)^t We Want R(t) for 2015 t = 2015 - 1996 = 19 R(19) = 220(1.143)^19 R(19) = 220 * 12.672969 [B]R(19) = 2788.05 ~ 2,788[/B]

sqrt(12)sqrt(6)/sqrt(8) Simplified, we have: sqrt(72)/sqrt(8) The top can be written as sqrt(8 * 9) which is sqrt(8) * sqrt(9) So we have: sqrt(8) * sqrt(9)/sqrt(8) Cancelling the sqrt(8), we have: [S]sqrt(8)[/S] * sqrt(9)/[S]sqrt(8)[/S] sqrt(9) =[B] 3[/B]

Square root of 9136 divided by 43 First, [URL=' the square root of 9136 in our calculator[/URL]: 4 * sqrt(571) Now divide this by 43: [B]4 * sqrt(571) / 43[/B]

square root of the sum of 2 variables The phrase [I]2 variables[/I] means we choose 2 arbitrary variables, let's call them x and y: x, y The sum of 2 variables means we add: x + y Square root of the sum of 2 variables is written as: [B]sqrt(x + y)[/B]

square root of x times the square root of y square root of x: sqrt(x) square root of y: sqrt(y) square root of x times the square root of y [B]sqrt(x) * sqrt(y)[/B]

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Free Square Roots and Exponents Calculator - Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following:* The square root of n denoted as √n * The square root of the fraction n/m denoted as √n/m * n raised to the x^th power denoted as n^x (Write without exponents) * n raised to the x^th power raised to the yth power denoted as (n^x)^y (Write without exponents) * Product of up to 5 square roots: √a√b√c√d√e * Write a numeric expression such as 8x8x8x8x8 in exponential form

Squaring a number equals 5 times that number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Squaring this number: x^2 5 times this number means we multiply by 5: 5x The phrase [I]equals[/I] means we set both expressions equal to each other: [B]x^2 = 5x [/B] <-- This is our algebraic expression If you want to solve for x, then we subtract 5x from each side: x^2 - 5x = 5x - 5x Cancel the 5x on the right side, leaving us with 0: x^2 - 5x = 0 Factor out x: x(x - 5) So we get x = 0 or [B]x = 5[/B]

Standard Error (margin of Error) = Standard Deviation / sqrt(n) 128 = 545/sqrt(n) Cross multiply: 128sqrt(n) = 545 Divide by 128 sqrt(n) = 4.2578125 Square both sides: [B]n = 18.1289672852 But we need an integer, so the answer is 19[/B]

Stanley bought a ruler and a yardstick for $1.25. If the yardstick cost 45 cents more than the ruler, what was the cost of the yardstick? Let r be the cost of the ruler Let y be the cost of the yardstick We're given 2 equations: [LIST=1] [*]r + y = 1.25 [*]y = r + 0.45 [/LIST] Substitute equation (2) into equation (1) for y r + r + 0.45 = 1.25 Solve for [I]r[/I] in the equation r + r + 0.45 = 1.25 [SIZE=5][B]Step 1: Group the r terms on the left hand side:[/B][/SIZE] (1 + 1)r = 2r [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2r + 0.45 = + 1.25 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 0.45 and 1.25. To do that, we subtract 0.45 from both sides 2r + 0.45 - 0.45 = 1.25 - 0.45 [SIZE=5][B]Step 4: Cancel 0.45 on the left side:[/B][/SIZE] 2r = 0.8 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2r/2 = 0.8/2 r = 0.4 Substitute r = 0.4 into equation (2) above: y = r + 0.45 y = 0.4 + 0.45 r = [B]0.85 [URL='

Start with q. Multiply by p. Add 3. Divide A Start with q: q Multiply by p: pq Add 3: pq + 3 Divide A means divide by A. We wrap pq + 3 in parentheses to divide by the sum (pq + 3)/A

Start with t , add 6, divide by 2, then subtract 5. Start with t: t Add 6: t + 6 Divide by 2: (t + 6)/2 [I]Add parentheses because we're dividing the [U]quantity[/U] by 2 [/I] Then subtract 5: [B](t + 6)/2 - 5[/B]

Start with x , subtract 6, then times by 3. We start with x: x Subtract 6: x - 6 The phrase [I]times by[/I] means we multiply (x - 6) by 3 [B]3(x - 6) [/B] <-- This is our algebraic expression If the problem asks you to multiply through, then you'd have: 3x - 18

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Steven has some money. If he spends $9, then he will have 3/5 of the amount he started with. Let the amount Steven started with be s. We're given: s - 9 = 3s/5 Multiply each side through by 5 to eliminate the fraction: 5(s - 9) = 5(3s/5) Cancel the 5's on the right side and we get: 5s - 45 = 3s To solve for s, we [URL=' this equation into our search engine[/URL] and we get: s = [B]22.5[/B]

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Storm Center 7 was tracking a cold front approaching Cedarburg. Before it rolled in, the temperature was 7F. Then, the temperature decreased by 9F. What was the temperature after the cold front rolled in? Using signed integers, we start with 7 below or -7 -7 The temperature decreased by 9 which means we subtract: -7 - 9 or -7 + (-9) [B]-16F or 16 below 0 [MEDIA=youtube]oJjEhkdnTxA[/MEDIA][/B]

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Students stuff envelopes for extra money. Their initial cost to obtain the information for the job was $140. Each envelope costs $0.02 and they get paid $0.03per envelope stuffed. Let x represent the number of envelopes stuffed. (a) Express the cost C as a function of x. (b) Express the revenue R as a function of x. (c) Determine analytically the value of x for which revenue equals cost. a) Cost Function [B]C(x) = 140 + 0.02x[/B] b) Revenue Function [B]R(x) = 0.03x[/B] c) Set R(x) = C(x) 140 + 0.02x = 0.03x Using our [URL=' solver[/URL], we get x = [B]14,000[/B]

Substitute the given values into given formula and solve for the unknown variable. S = 4LW + 2 WH; S= 144, L= 8, W= 4. H= S = 4LW + 2 WH Substituting our given values, we have: 144 = 4(8)(4) + 2(4)H 144 = 128 + 8H Using our [URL=' calculator[/URL], we get: [B]H = 2[/B]

Sum of w and v: w + v Square that sum (w + v)^2 Subtract 12 from the squared sum (w + v)^2 - 12

Subtract 4 from the sum of 2x and 5y. The sum of 2x and 5y means we add both terms: 2x + 5y Subtract 4 from this sum to get our algebraic expression: [B](2x + 5y) - 4[/B]

Subtract 7 from p, then multiply 5 by the result. Subtract 7 from p p - 7 Multiply 5 by the result: [B]5(p - 7)[/B]

subtract q from r, then subtract 6 from the result Subtract q from r r - q Then subtract 6 from the results [B](r - q) - 6[/B]

subtract s from q, subtract the result from r, then double what you have Subtract s from q: q - s Subtract the result from r: r - (q - s) Then double what you have: [B]2(r - (q - s))[/B]

subtract the difference of t and s from 8 The difference of t and s: t - s Subtract this from 8: 8 - (t - s)

subtract w from u, triple the result, then multiply v by what you have Take this algebraic expression in 3 parts: [U]1) subtract w from u:[/U] u - w [U]2) Triple the result means we multiply u - w by 3:[/U] 3(u - w) [U]3) Multiply v by what you have. [I]What you have[/I] means the result from step 2:[/U] [B]3v(u - w)[/B]

subtract w from v, add the result to u, then triple what you have Take this algebraic expression in parts: [LIST=1] [*]Subtract w from v: v - w [*]Add the result to u (the result is #1): u + v - w [*]Triple what you have. This means multiply the result in #2 by 3: [/LIST] [B]3(u + v - w)[/B]

sum of 3 consecutive odd integers equals 1 hundred 17 The sum of 3 consecutive odd numbers equals 117. What are the 3 odd numbers? 1) Set up an equation where our [I]odd numbers[/I] are n, n + 2, n + 4 2) We increment by 2 for each number since we have [I]odd numbers[/I]. 3) We set this sum of consecutive [I]odd numbers[/I] equal to 117 n + (n + 2) + (n + 4) = 117 [SIZE=5][B]Simplify this equation by grouping variables and constants together:[/B][/SIZE] (n + n + n) + 2 + 4 = 117 3n + 6 = 117 [SIZE=5][B]Subtract 6 from each side to isolate 3n:[/B][/SIZE] 3n + 6 - 6 = 117 - 6 [SIZE=5][B]Cancel the 6 on the left side and we get:[/B][/SIZE] 3n + [S]6[/S] - [S]6[/S] = 117 - 6 3n = 111 [SIZE=5][B]Divide each side of the equation by 3 to isolate n:[/B][/SIZE] 3n/3 = 111/3 [SIZE=5][B]Cancel the 3 on the left side:[/B][/SIZE] [S]3[/S]n/[S]3 [/S]= 111/3 n = 37 Call this n1, so we find our other 2 numbers n2 = n1 + 2 n2 = 37 + 2 n2 = 39 n3 = n2 + 2 n3 = 39 + 2 n3 = 41 [SIZE=5][B]List out the 3 consecutive odd numbers[/B][/SIZE] ([B]37, 39, 41[/B]) 37 ? 1st number, or the Smallest, Minimum, Least Value 39 ? 2nd number 41 ? 3rd or the Largest, Maximum, Highest Value

Sum of a number and 7 is subtracted from 15 the result is 6. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We take this expression in pieces. Sum of a number and 7 x + 7 Subtracted from 15 15 - (x + 7) The result is means an equation, so we set this expression above equal to 6 [B]15 - (x + 7) = 6 <-- This is our algebraic expression[/B] If the problem asks you to solve for x, we Group like terms 15 - x - 7 = 6 8 - x = 6 [URL=' 8 - x = 6 into the search engine[/URL], and we get [B]x = 2[/B]

Sum of N and its next consecutive even integer is 65 Next even consecutive integer is N + 2. We have N + (N + 2) = 65. Combine like terms, we have 2N + 2 = 65 [URL=' this problem through the search engine[/URL], we get n = 31.5. Meaning this problem is impossible, it cannot be done. n is not an integer, and neither is the next consecutive even integer.

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Sum of two consecutive numbers is always odd Definition: [LIST] [*]A number which can be written in the form of 2 m where m is an integer, is called an even integer. [*]A number which can be written in the form of 2 m + 1 where m is an integer, is called an odd integer. [/LIST] Take two consecutive integers, one even, and one odd: 2n and 2n + 1 Now add them 2n + (2n+ 1) = 4n + 1 = 2(2 n) + 1 The sum is of the form 2n + 1 (2n is an integer because the product of two integers is an integer) Therefore, the sum of two consecutive integers is an odd number.

sum of x plus y divided by 2 sum of x plus y: x + y sum of x plus y divided by 2 [B](x + y)/2[/B]

Free Sum to Product and Product to Sum Formulas Calculator - Given two angles in degrees of u and v, this determines the following: * Sin(u) ± Sin(v) * Cos(u) ± Cos(v) * Sin(u)Sin(v) * Cos(u)Cos(v) * Sin(u)Cos(v) * Cos(u)Sin(v) * Sin(u + v) * Sin(u - v) * Cos(u + v) * Cos(u - v) * Tan(u + v) * Tan(u - v)

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the population of the city in 7 years Set up the population function P(y) where y is the number of years since now: P(y) = Current population + Growth per year * y Plugging in our numbers at y = 7, we get: P(7) = 740000 + 12620(7) P(7) = 740000 + 88340 P(7) = [B]828,340[/B]

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the population of the city in 7 years. We setup the population function P(y) where y is the number of years of population growth, g is the growth per year, and P(0) is the original population. P(y) = P(0) + gy Plugging in our numbers of y = 7, g = 12,620, and P(0) = 740,000, we have: P(7) = 740,000 + 12,620 * 7 P(7) = 740,000 + 88,340 P(7) = [B]828,340[/B]

Suppose a firm producing light bulbs wants to know if it can claim that its light bulbs it produces last 1,000 burning hours (u). To do this, the firm takes a random sample of 100 bulbs and find its average life time (X=980 hrs) and the sample standard deviation s = 80 hrs. If the firm wants to conduct the test at the 1% of significance, what's you final suggestion? (i..e, Should the producer accept the Ho that its light bulbs have a 1,000 burning hrs. at the 1% level of significance?) Ho: u = 1,000 hours. Ha: u <> 1,000 hours. [URL=' a hypothesis test of the mean[/URL] [B]Yes, accept null hypothesis[/B]

Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin does she have? Set up two equations where d is the number of dimes and q is the number of quarters: (1) d + q = 10 (2) 0.1d + 0.25q = 1.45 Rearrange (1) into (3) to solve for d (3) d = 10 - q Now plug (3) into (2) 0.1(10 - q) + 0.25q = 1.45 Multiply through: 1 - 0.1q + 0.25q = 1.45 Combine q terms 0.15q + 1 = 1.45 Subtract 1 from each side 0.15q = 0.45 Divide each side by 0.15 [B]q = 3[/B] Plug our q = 3 value into (3) d = 10 - 3 [B]d = 7[/B]

Suppose Rocky Mountain have 72 centimeters of snow. Warmer weather is melting at the rate of 5.8 centimeters a day. If snow continues to melt at this rate, after seven days of warm weather, how much snow will be left? Snow remaining = Starting snow - melt rate * days Snow remaining = 72 - 5.8(7) Snow remaining = 72 - 40.6 Snow remaining = [B]31.4 cm[/B]

Suppose that 18% of people own dogs. If you pick two people at random, what is the probability that they both own a dog? Since each person is independent of the others, we have: P(Person 1 has a dog and person 2 have a dog) = P(person 1 has a dog) * P(person 2 has a dog) P(Person 1 has a dog and person 2 have a dog) = 0.18 * 0.18 P(Person 1 has a dog and person 2 have a dog) = [B]0.0324 or 3.24%[/B]

Suppose that h(x) varies directly with x and h(x)=44 when x = 2. What is h(x) when x = 1.5? Direct variation means we set up an equation: h(x) = kx where k is the constant of variation. For h(x) = 44 when x = 2, we have: 2k = 44 [URL=' this equation into our search engine[/URL], we get: k = 22 The question asks for h(x) when x = 1.5. So we set up our variation equation, knowing that k = 22. kx = h(x) With k = 22 and x = 1.5, we get: 22(1.5) = h(x) h(x) = [B]33[/B]

Suppose that previously collected traffic data indicate that, during the afternoon rush hour, an average of 4 cars arrive at a toll bridge each second. If it is assumed that cars arrive randomly, and can thus be modeled with Poisson distribution, what is the probability that in the next second, [U][B]NO[/B][/U] cars will arrive? Use the [I]Poisson Distribution[/I] with λ = 4 and x = 0 Using the [URL=' Distribution calculator[/URL], we get P(0; 4) = [B]0.0183[/B]

Suppose that Sn = 3 + 1/3 + 1/9 + ... + 1/3(n-2) a) Find S10 and S? b) If the common difference in an arithmetic sequence is twice the first term, show that Sn/Sm = n^2/m^2 a) Sum of the geometric sequence is a = 3 and r = 1/3 (a(1 - r)^n)/(1 - r) (3(1 - 1/3)^9)/(1 - 1/3) [B]S10 = 4.499771376[/B] For infinity, as n goes to infinity, the numerator goes to 1 so we have [B]S? = 3(1)/2/3 = 4.5[/B] b) Sum of an arithmetic sequence formula is below: n(a1 + an)/2 an = a1 + (n - 1)2a1 since d = 2a1 n(a1 + a1 + (n - 1)2a1)/2 (2a1n + n^2 - 2a1n)/2 n^2/2 For Sm m(a1 + am)/2 am = a1 + (m - 1)2a1 since d = 2a1 m(a1 + 1 + (m - 1)2a1)/2 (2a1m + m^2 - 2a1m)/2 m^2/2 Sn/Sm = n^2/m^2 (cancel the 2's) S10/S1 = 10^2/1^2 We know S₁ = 3 So we have 100(3)/1 [B]S10 = 300[/B]

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______)b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.c. Find the 80^th percentile of the distribution of the average of 49 fly balls a. N(250, 50/sqrt(49)) = [B]0.42074[/B] b. Calculate Z-score and probability = 0.08 shown [URL=' c. Inverse of normal distribution(0.8) = 0.8416. Use NORMSINV(0.8) [URL=' Using the Z-score formula, we have 0.8416 = (x - 250)/50 x = [B]292.08[/B]

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. a. If X = distance in feet for a fly ball, then X ~ b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability. c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement. a. [B]N(250, 50/sqrt(1))[/B] b. Calculate [URL=' Z = -0.6 and P(Z < -0.6) = [B]0.274253[/B] c. Inverse of normal distribution(0.8) = 0.8416 using NORMSINV(0.8) [URL=' Z-score formula: 0.8416 = (x - 250)/50x = [B]292.08[/B]

Suppose that the manager of the Commerce Bank at Glassboro determines that 40% of all depositors have a multiple accounts at the bank. If you, as a branch manager, select a random sample of 200 depositors, what is the probability that the sample proportion of depositors with multiple accounts is between 35% and 50%? [URL=' proportion probability[/URL]: z = 2.04124145232 [URL=' proportion probability[/URL]: z = -1.02062072616 Now use the [URL='

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 20 gallons of fuel, the airplane weighs 2012 pounds. When carrying 55 gallons of fuel, it weighs 2208 pounds. How much does the airplane weigh if it is carrying 65 gallons of fuel? Linear functions are written in the form of one dependent variable and one independent variable. Using g as the number of gallons and W(g) as the weight, we have: W(g) = gx + c where c is a constant We are given: [LIST] [*]W(20) = 2012 [*]W(55) = 2208 [/LIST] We want to know W(65) Using our givens, we have: W(20) = 20x + c = 2012 W(55) = 55x + c = 2208 Rearranging both equations, we have: c = 2012 - 20x c = 2208 - 55x Set them both equal to each other: 2012 - 20x = 2208 - 55x Add 55x to each side: 35x + 2012 = 2208 Using our [URL=' solver[/URL], we see that x is 5.6 Plugging x = 5.6 back into the first equation, we get: c = 2012 - 20(5.6) c = 2012 - 112 c = 2900 Now that we have all our pieces, find W(65) W(65) = 65(5.6) + 2900 W(65) = 264 + 2900 W(65) = [B]3264[/B]

Suppose that you have just purchased a car for $40,000. Historically, the car depreciates by 8% each year, so that next year the car is worth $40000(.92). What will the value of the car be after you have owned it for three years? Book Value B(t) at time t is B(t) = 40,000(1-0.08)^t or B(t) = 40,000(0.92)^t At t = 3 we have: B(3) = 40,000(0.92)^3 B(3) = 40,000 * 0.778688 B(3) = [B]31,147.52[/B]

List out the sums greater than 8: (4, 5) (4, 6) (5, 5) (5, 6) (6, 6) (5, 4) (6, 4) (6, 5) Since there are 6 * 6 = 36 total outcomes, we have the probability of the sum greater than 8 as: 8/36 = 2/9

Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6. When you divide x by 11 you get the same quotient but a remainder of 2. Find x. [U]Use the quotient remainder theorem[/U] A = B * Q + R where 0 ? R < B where R is the remainder when you divide A by B Plugging in our numbers for Equation 1 we have: [LIST] [*]A = x [*]B = 7 [*]Q = q [*]R = 6 [*]x = 7 * q + 6 [/LIST] Plugging in our numbers for Equation 2 we have: [LIST] [*]A = x [*]B = 11 [*]Q = q [*]R = 2 [*]x = 11 * q + 2 [/LIST] Set both x values equal to each other: 7q + 6 = 11q + 2 Using our [URL=' calculator[/URL], we get: q = 1 Plug q = 1 into the first quotient remainder theorem equation, and we get: x = 7(1) + 6 x = 7 + 6 [B]x = 13[/B] Plug q = 1 into the second quotient remainder theorem equation, and we get: x = 11(1) + 2 x = 11 + 2 [B]x = 13[/B]

Suppose you deposit $3000 in an account paying 2% annual interest, compounded continuously. Use A=Pert to find the balance after 5 years. A = $3,000 * e^0.02(5) A = $3,000 * e^0.1 A = $3,000 * 1.105171 A = [B]$3,315.51[/B]

Suppose you have $28.00 in your bank account and start saving $18.25 every week. Your friend has $161.00 in his account and is withdrawing $15 every week. When will your account balances be the same? Set up savings and withdrawal equations where w is the number of weeks. B(w) is the current balance [LIST] [*]You --> B(w) = 18.25w + 28 [*]Your friend --> B(w) = 161 - 15w [/LIST] Set them equal to each other 18.25w + 28 = 161 - 15w [URL=' that problem into the search engine[/URL], and you get [B]w = 4[/B].

Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on advertising. You sell the book for $15 a copy. How many copies must you sell to break even. Profit per book is: P = 15 - 4 P = 11 We want to know the number of books (b) such that: 11b = 5500 <-- Breakeven means cost equals revenue [URL=' this equation into the search engine[/URL], we get: b = [B]500[/B]

Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each. This Saturday, she is renting a booth at a craft fair for $50. Write an equation that can be used to find the number of purses Susan must sell to make a profit of $295 Set up the cost function C(p) where p is the number of purses: C(p) = Cost per purse * p + Booth Rental C(p) = 15p + 50 Set up the revenue function R(p) where p is the number of purses: R(p) = Sale price * p R(p) = 30p Set up the profit function which is R(p) - C(p) equal to 295 30p - (15p + 50) = 295 To solve this equation, [URL=' type it into our search engine[/URL] and we get: p = [B]23[/B]

Free Synthetic Division Calculator - Using Ruffinis Rule, this performs synthetic division by dividing a polynomial with a maximum degree of 6 by a term (x ± c) where c is a constant root using the factor theorem. The calculator returns a quotient answer that includes a remainder if applicable. Also known as the Rational Zero Theorem

T = mg - mf for f Subtract mg from each side: T - mg = mg - mg - mf Cancel the mg on the right side and we get: T - mg = -mf Multiply each side by -1: -(T - mg) = -(-mf) mg - T = mf Now Divide each side by m to isolate f: (mg - T)/m = mf/m Cancel the m on the right side and we get: f = [B](mg - T)/m[/B]

Free T-Bill Calculator - Calculates any of the four items of the T-Bill (Treasury Bill or TBill) formula:1) Price (P)2) Face Value (F)3) Number of Weeks (w)4) Yield Rate (y)

T-shirts sell for $19.97 and cost $14.02 to produce. Which equation represents p, the profit, in terms of x, the number of t-shirts sold? A) p = $19.97x - $14.02 B) p = x($19.97 - $14.02) C) p = $19.97 + $14.02x D) p = x($19.97 + $14.02) [B]B) p = x($19.97 - $14.02)[/B] [B][/B] [LIST] [*]Profit is Revenue - Cost [*]Each shirt x generates a profit of 19.97 - 14.02 [/LIST]

Free Tabular Display Calculator - Enter a set of x and p(x) in a tabular probability distribution format and this will evaluate if it is valid or not.

Take a look at the following sums: 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = 25 a. Come up with a conjecture about the sum when you add the first n odd numbers. For example, when you added the first 5 odd numbers (1 + 3 + 5 + 7 + 9), what did you get? What if wanted to add the first 10 odd numbers? Or 100? b. Can you think of a geometric interpretation of this pattern? If you start with one square and add on three more, what can you make? If you now have 4 squares and add on 5 more, what can you make? c. Is there a similar pattern for adding the first n even numbers? 2 = 2 2 + 4 = 6 2 + 4 + 6 = 12 2 + 4 + 6 + 8 = 20 a. The formula is [B]n^2[/B]. The sum of the first 10 odd numbers is [B]100[/B] seen on our s[URL=' of the first calculator[/URL] The sum of the first 100 odd numbers is [B]10,000[/B] seen on our [URL=' of the first calculator[/URL] b. Geometric is 1, 4, 9 which is our [B]n^2[/B] c. The sum of the first n even numbers is denoted as [B]n(n + 1)[/B] seen here for the [URL=' 10 numbers[/URL]

Free Tally Marks Calculator - Shows the tally mark representation (tallies) for a positive integer.

Tamira and her 3 friends spent a total of $37 for a large pizza and 4 sodas. Each soda cost $2. Which equation can be used to find p, the cost of the pizza? We add the cost of the pizza (p) to the 4 sodas @ $2 each to get 37 p + 4(2) = 37 [B]p + 8 = 37 (This is the equation) [/B] If the problem asks you to solve for p, then we [URL=' the equation above into our search engine[/URL] and we get: p = [B]29[/B]

Free Target Heart Rate Calculator - Given an age, this calculator determines the following 5 target heart rate zones:Healthy Heart Zone (Warm up) 50 - 60%Fitness Zone (Fat Burning) 60 - 70%Aerobic Zone (Endurance Training) 70 - 80%Anaerobic Zone (Performance Training) 80 - 90%Red Line (Maximum Effort) 90 - 100%

Taylor is playing a game using a die and a spinner. The spinner is divided into 4 equal parts with colors green, red, yellow, and purple. Taylor rolls the die and spins the spinner. What is the probability the die shows a 2 and the spinner lands on purple? Probability of rolling a 2 on the die is 1/6 Probability of getting a purple on the spinner is 1/4 Since each event is independent, our joint probability is: P(2 on the die and Purple on the spinner) = P(2 on the die) x P(Purple on the Spinner) P(2 on the die and Purple on the spinner) = 1/6 x 1/4 P(2 on the die and Purple on the spinner) = [B]1/24[/B]

Free Ten Frame Calculator - Builds a ten frame (dot card) for a number and shows numbers more and less.

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. Twice a number means we multiply x by 2: 2x The sum of twice a number and 6: 2x + 6 Ten times the sum of twice a number and six [B]10(2x + 6)[/B]

Terry recorded the temperature every hour from 8 AM to 1 PM. The temperature at 8 AM was 19?. The temperature dropped 4? every hour. What was the temperature at 1 PM? Group of answer choices 1 degree Set up our temperature function T(h) where h is the number of hours since 8 AM: T(h) = 19 - 4h <-- We subtract 4h since each hour, the temperature drops 4 degrees The questions asks for the temperature at 1PM. We need to figure out how many hours pass since 8 AM: 8 AM to 12 PM is 4 hours 12 PM to 1 PM is 1 hour Total time is 5 hours So we want T(5): T(5) = 19 - 4(5) T(5) = 19 - 20 T(5) = [B]-1?[/B]

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. What is the value of N ? Average of the first number set is [URL=' our average calculator[/URL] is: 36 Now, the mean (average) or 19 and N is found by adding them together an dividing by 2: (19 + N)/2 Since both number sets have equal means, we set (19 + N)/2 equal to 36: (19 + N)/2 = 36 Cross multiply: 19 + N = 36 * 2 19 + n = 72 To solve for n, we [URL=' this equation into our search engine[/URL] and we get: n = [B]53[/B]

The auditorium can hold a maximum of 150 people We want an inequality for the number of people (p) in the auditorium. The word [I]maximum[/I] means [I]no more than[/I] or [I]less than or equal to[/I]. So we have: [B]p <= 150[/B]

The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the number of books printed that day and k is a constant. Find k, if on the day when 200 were printed the average cost was $9 per book. We are given: c(200) = 9, so we have: 9 = 5.5(200) + k(200) 200k + 1100 = 9 Using our [URL=' solver[/URL], we get: [B]k = -5.455[/B]

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother? [LIST] [*]Let the height of the family without the mom be f. Let the height of the mother be m. [*]Averages mean we add the heights and divide by the number of people who were measured. [/LIST] We're given two equations: [LIST=1] [*](f + m)/6 = 6 [*]f/5 = 6 [/LIST] Cross multiplying equation (2), we get: f = 5 * 6 f = 30 Plug f = 30 into equation (1), we get: (30 + m)/6 = 6 Cross multiplying, we get: m + 30 = 6 * 6 m + 30 = 36 To solve this equation for m, we [URL=' it in our search engine[/URL] and we get: m = [B]6[/B] [SIZE=3][FONT=Arial][COLOR=rgb(34, 34, 34)][/COLOR][/FONT][/SIZE]

The average of 16 and x is 21. Find x. The average of 2 numbers is the sum of the 2 numbers divided by 2. So we have: (16 + x)/2 = 21 Cross multiply: 16 + x = 21*2 16 + x = 42 To solve this equation, [URL=' type this expression into the search engine[/URL] and get [B]x = 26[/B]. Check our work by restating our answer: The average of 16 and 26 is 21. TRUE.

The average of 171 and x? The phrase [I]average[/I] means add up all the items in the number set, divided by the count of items in the number set. Our number set in this case is {171, x} which has 2 elements. Therefore, our average is: [B](171 + x)/2[/B]

The average of 20 numbers is 18 while the average of 18 numbers is 20. What is the average of the 38 numbers? The average of averages is found by getting the sum of both groups of numbers and dividing by the count of numbers. Calculate the sum of the first group of numbers S1: Average = S1 / n1 18 = S1 / 20 S1 = 20 * 18 S1 =360 Calculate the sum of the second group of numbers S2: Average = S2 / n2 20 = S2 / 18 S2 = 18 * 20 S2 =360 Our average of averages is found by the following: A = (S1 + S2)/(n1 + n2) A = (360 + 360)/(20 + 18) A = 720/38 [B]A = 18.947[/B]

Let x equal "a number". Double the number is 2x. The average is (x + 2x)/2 Combine the terms in the numerator: 3x/2 The word [I]is[/I] means equal to, so we set 3x/2 equal to 25.5 3x/2 = 25.5 Cross multiply the 2: 3x = 51 Divide each side by 3 [B]x = 17[/B]

the average of eighty-five and a number m is ninety Average of 2 numbers means we add both numbers and divide by 2: (85 + m)/2 = 90 Cross multiply: m + 85 = 90 * 2 m + 85 = 180 To solve this equation for m, we [URL=' it in our math engine [/URL]and we get: m = [B]95[/B]

the average of two numbers x and y Average is the sum divided by the count: Sum: x + y We have 2 numbers, so we divide (x + y) by 2 [B](x + y)/2[/B]

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed. a. What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months? b. What is the average precipitation of 5 randomly selected years for the first 7 months? c. What is the probability of 5 randomly selected years will have an average precipitation greater than 18 inches for the first 7 months? [URL=' a. we set up our z-score for[/URL]: P(X>18) = 0.7088 b. We assume the average precipitation of 5 [I]randomly[/I] selected years for the first 7 months is the population mean ? = 19.32 c. [URL='(X > 18 with n = 5)[/URL] = 0.8907

The basketball team is selling candy as a fundraiser. A regular candy bar cost 0.75 and a king sized candy bar costs 1.50. In the first week of the sales the team made 36.00. Exactly 12 regular sized bars were sold that week. How many king size are left? Let r be the number of regular bars and k be the number of king size bars. Set up our equations: [LIST=1] [*]0.75r + 1.5k = 36 [*]r = 12 [/LIST] [U]Substitute (2) into (1)[/U] 0.75(12) + 1.5k = 36 9 + 1.5k = 36 [U]Use our equation solver, we get:[/U] [B]k = 18[/B]

The bigger of 2 numbers in 5 larger than the smaller. Twice the smaller, increased by, twice the larger, is equal to 50. Find each number. Let the big number be b. Let the small number be s. We're given two equations: [LIST=1] [*]b = s + 5 [*]2s + 2b = 50 [/LIST] Substitute equation (1) into equation (2) 2s + 2(s + 5) = 50 [URL=' this equation into our search engine[/URL], and we get: [B]s = 10[/B] Now substitute s = 10 into equation (1) to solve for b: b = 10 + 5 [B]b = 15[/B]

The blue star publishing company produces daily "Star news". It costs $1200 per day to operate regardless of whether any newspaper are published. It costs 0.20 to publish each newspaper. Each daily newspaper has $850 worth of advertising and each newspaper is sold for $.30. Find the number of newspaper required to be sold each day for the Blue Star company to 'break even'. I.e all costs are covered. Build our cost function where n is the number of newspapers sold: C(n) = 1200+ 0.2n Now build the revenue function: R(n) = 850 + 0.3n Break even is where cost and revenue are equal, so set C(n) = R(n) 1200+ 0.2n = 850 + 0.3n Using our [URL=' solver[/URL], we get: [B]n = 3,500[/B]

the book is 11 inches long, 11 inches wide, and 2 inches thick. find the volume of the book The book is a rectangular solid, so our Volume (V) is: V = l * w * h V = 11 * 11 * 2 V = [B]242 cubic inches[/B]

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the bran. How many adults must he survey in order to be 90% confident that his estimate is within seven percentage points of the true population percentage? [IMG] = 0.5 1 - [IMG] = 0.5 margin of error (E) = 0.07 At 90% confidence level the t is, alpha = 1 - 90% alpha = 1 - 0.90 alpha = 0.10 alpha / 2 = 0.10 / 2 = 0.05 Zalpha/2 = Z0.05 = 1.645 sample size = n = (Z[IMG] / 2 / E )2 * [IMG] * (1 - [IMG] ) = (1.645 / 0.07)^2 *0.5*0.5 23.5^2 * 0.5 * 0.5 552.25 * 0.5 * 0.5 = 138.06 [B]sample size = 138[/B] [I]He must survey 138 adults in order to be 90% confident that his estimate is within seven percentage points of the true population percentage.[/I]

The buyer of a lot pays P10,000 every month for 10 years. If the money is 8% compounded annually, how much is the cash value of the lot? (use j= 0.006434, n=120) Using our [URL=' interest calculator[/URL], we get: [B]22,196.40[/B]

The charge to rent a trailer is $30 for up to 2 hours plus $9 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.4 hours, 3 hours, and 8.5 hours. Set up the cost function C(h), where h is the number of hours to rent the trailer. We have, for any hours greater than 2: C(h) = 30 + 9(h - 2) Simplified, we have: C(h) = 9h - 18 + 30 C(h) = 9h + 12 The question asks for C(2.4), C(3), and C(8.5) [U]Find C(2.4)[/U] C(2.4) = 9(2.4) + 12 C(2.4) = 21.6 + 12 C(2.4) = [B]33.6 [/B] [U]Find C(3)[/U] C(3) = 9(3) + 12 C(3) = 27 + 12 C(2.4) = [B][B]39[/B][/B] [U]Find C(8.5)[/U] C(8.5) = 9(8.5) + 12 C(8.5) = 76.5 + 12 C(8.5) = [B]88.5[/B]

The club uses the function S(t) = -4,500t + 54,000 to determine the salvage S(t) of a fertilizer blender t years after its purchase. How long will it take the blender to depreciate completely? Complete depreciation means the salvage value is 0. So S(t) = 0. We need to find t to make S(t) = 0 -4,500t + 54,000 = 0 Subtract 54,000 from each side -4,500t = -54,000 Divide each side by -4,500 [B]t = 12[/B]

The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the total cost to park for 5 hours? Set up our equation where C is cost and h is the number of hours used to park C = 1.5h + 2.25 With h = 5, we have: C = 1.5(5) + 2.25 C = 7.5 + 2.25 C = 9.75

The cost of a field trip is $220 plus $7 per student. If the school can spend at most $500, how many students can go on the field trip? Set up the inequality where s is the number of students: C(s) = 220 + 7s We want C(s) <= 500, since at most means no more than 220 + 7s <= 500 Using our [URL=' calculator[/URL], we get: [B]s <= 40[/B]

The cost of a gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a gallon of milk cost 3.75, what is the cost of a gallon of water? We're given: m = 5w + 0.50 m = $3.75 Set them equal to each other: 5w + 0.50 = 3.75 [URL=' this equation into our search engine[/URL], we get: [B]w = 0.65[/B]

The cost of a taxi ride is $1.2 for the first mile and $0.85 for each additional mile or part thereof. Find the maximum distance we can ride if we have $20.75. We set up the cost function C(m) where m is the number of miles: C(m) = Cost per mile after first mile * m + Cost of first mile C(m) = 0.8(m - 1) + 1.2 C(m) = 0.8m - 0.8 + 1.2 C(m) = 0.8m - 0.4 We want to know m when C(m) = 20.75 0.8m - 0.4 = 20.75 [URL=' this equation into our math engine[/URL], we get: m = 26.4375 The maximum distance we can ride in full miles is [B]26 miles[/B]

The cost of having a plumber spend h hours at your house if the plumber charges $60 for coming to the house and $70 per hour labor: We have a fixed cost of $60 plus the variable cost of $70h. We add both for our total cost C(h): [B]C(h) = $70h + 60[/B]

The cost of hiring a car for a day is $60 plus 0.25 cents per kilometer. Michelle travels 750 kilometers. What is her total cost Set up the cost function C(k) where k is the number of kilometers traveled: C(k) = 60 + 0.25k The problem asks for C(750) C(750) = 60 + 0.25(750) C(750) = 60 + 187.5 C(750) = [B]247.5[/B]

the cost of x concert tickets if one concert ticket costs $97 The cost function C(x), where x is the number of concert tickets is: [B]C(x) = 97x[/B]

The cost of x ice cream if one ice cream cost $9 and the fixed cost is $8142 Cost function is C(x) is: C(x) = Cost per ice cream * number of ice creams + Fixed Cost C(x) = [B]9x + 8142[/B]

the cost of x pounds of pork at $4.10 a pound Set up the cost function for pounds of pork: [B]C(x) = 4.10x[/B]

The cost of x textbooks if one textbook costs $140. Set up a cost function where x is the number of textbooks: [B]C(x) = 140x[/B]

The cost to rent a boat is $10. There is also charge of $2 for each person. Which expresion represents the total cost to rent a boat for p persons? The cost function includes a fixed cost of $10 plus a variable cost of 2 persons for p persons: [B]C(p) = 2p + 10[/B]

The cost to rent a construction crane is 450 per day plus 150 per hour. What is the maximum number of hours the crane can be used each day if the rental cost is not to exceed 1650 per day? Set up the cost function where h is the number of hours: C(h) = 150h + 450 We want C(h) <= 1650: 150h + 450 <= 1650 Using our [URL=' solver[/URL], we get: [B]h <= 8[/B]

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y Take this in algebraic expression in parts: [U]Term 1[/U] [LIST] [*]The square of y means we raise y to the 2nd power: y^2 [*]5 times the square of y: 5y^2 [/LIST] [U]Term 2[/U] [LIST] [*]2 times y: 2y [*]The square of 2 times y: (2y)^2 = 4y^2 [*]7 divide by the square of 2 times y: 7/4y^2 [/LIST] [U]The difference of these terms is written as Term 1 minus Term 2:[/U] [LIST] [*]5y^2/4y^2 [/LIST] [U]The cube of the difference means we raise the difference to the power of 3:[/U] [B](5y^2/4y^2)^3[/B]

the cube of the difference of 5 times x and 4 Take this algebraic expression in pieces: 5 times x: 5x The difference of 5x and 4 means we subtract 4 from 5x: 5x - 4 We want to cube this difference, which means we raise the difference to the power of 3. [B](5x - 4)^3[/B]

the cube of the product of 3 and x The product of 3 and x: 3x Cube this product means raise it to the power of 3: (3x)^3 = [B]27x^3[/B]

the cube of the sum of 2a and 3b Sum of 2a and 3b: (2a + 3b) The cube of the sum mean we raise the sum to the power of 3: [B](2a + 3b)^3[/B]

The dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for each ticket sold they sell to the Spring Fling dance. The dance will cost $400 Let t be the number of tickets sold. We have a Revenue function R(t): R(t) = 4t + 72 We want to know t such that R(t) = 400. So we set R(t) = 400: 4t + 72 = 400 [URL=' this equation into our search engine[/URL], we get: [B]t = 82[/B]

The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is added to the denominator, the value of the fraction is 1/2. Find the original fraction. Let the original fraction be n/d. We're given: [LIST=1] [*]d = n + 4 [*](n + 4) / (d + 7) = 1/2 [/LIST] Cross multiply Equation 2: 2(n + 4) = d + 7 2n + 8 = d + 7 Now substitute equation (1) into tihs: 2n + 8 = (n + 4) + 7 2n + 8 = n + 11 [URL=' this equation into our search engine[/URL], and we get: n = 3 This means from equation (1), that: d = 3 + 4 d = 7 So our original fraction n/d = [B]3/7[/B]

Draw this rectangle and you'll see we have a pythagorean theorem equation. a^2 + b^2= c^2 b = 8 and c= 10 a^2 + 8^2 = 10^2 a^2 + 64 = 100 Subtract 64 from each side: a^2 = 36 a= 6 Therefore, perimeter P is: P = 2l + 2w P = 2(6) + 2(8) P = 12 + 16 P = [B]28[/B] [MEDIA=youtube]8lcpRet3r18[/MEDIA]

The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. What are the numbers? Let the smaller number be x. Let the larger number be y. We're given: [LIST=1] [*]y - x = 108 [*]6x = y + 2 [/LIST] Rearrange (1) by adding x to each side: [LIST=1] [*]y = x + 108 [/LIST] Substitute this into (2): 6x = x + 108 + 2 Combine like terms 6x = x +110 Subtract x from each side: 5x = 110 [URL=' this equation into our search engine[/URL], we get: x = [B]22[/B]

the difference between 7 times a number and 9 less than a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 7 times a number means we multiply x by 7 7x 9 less than a number means we subtract 9 from x x - 9 The difference between the two expressions means we subtract (x - 9) from 7x 7x - (x - 9) Simplifying this, we have: 7x - x + 9 Grouping like terms, we get: [B]6x + 9[/B]

The difference between the square of b and the total of b and 9 The square of b means we raise b to the power of 2: b^2 The total of b and 9 means we add 9 to b: b + 9 The difference means we subtract: [B]b^2 - (b + 9)[/B]

The difference between the square of b and the total of d and g Square of b means we raise b to the 2nd power: b^2 Total of d and g: d + g The difference between the square of b and the total of d and g [B]b^2 - (d + g)[/B]

The difference between the squares of two consecutive numbers is 141. Find the numbers Take two consecutive numbers: n- 1 and n Given a difference (d) between the squares of two consecutive numbers, the shortcut for this is: 2n - 1 = d Proof of this: n^2- (n - 1)^2 = d n^2 - (n^2 - 2n + 1) = d n^2 - n^2 + 2n - 1 = d 2n - 1 = d Given d = 141, we have 2n - 1 = 141 Add 1 to each side: 2n = 142 Divide each side by 2: 2n/2 = 142/2 n = [B]71[/B] Therefore, n - 1 = [B]70 Our two consecutive numbers are (70, 71)[/B] Check your work 70^2 = 4900 71^2 = 5041 Difference = 5041 - 4900 Difference = 141 [MEDIA=youtube]vZJtZyYWIFQ[/MEDIA]

the difference between triple a number and double a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Triple a number means we multiply x by 3: 3x Double a number means we multiply x by 2: 2x The difference means we subtract 2x from 3x: 3x - 2x Simplifying like terms, we have: (3 - 2)x = [B]x[/B]

The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number Let the smaller number be s. Let the larger number be l. We're given two equations: [LIST=1] [*]l - s = 25 [*]s = l/6 [/LIST] Plug in equation (2) into equation (1): l - l/6 = 25 Multiply each side of the equation by 6 to remove the fraction: 6l - l = 150 To solve for l, we [URL=' this equation into our search engine[/URL] and we get: l = 30 To solve for s, we plug in l = 30 into equation (2) above: s = 30/6 [B]s = 5[/B]

The difference between two numbers is 96. One number is 9 times the other. What are the numbers? Let x be the first number Let y be the second number We're given two equations: [LIST=1] [*]x - y = 96 [*]x = 9y [/LIST] Substitute equation (2) into equation (1) for x 9y - y = 96 [URL=' this equation into our math engine[/URL], we get: y = [B]12 [/B] If y = 12, then we plug this into equation 2: x = 9(12) x = [B]108[/B]

The difference between two positive numbers is 5 and the square of their sum is 169. Let the two positive numbers be a and b. We have the following equations: [LIST=1] [*]a - b = 5 [*](a + b)^2 = 169 [*]Rearrange (1) by adding b to each side. We have a = b + 5 [/LIST] Now substitute (3) into (2): (b + 5 + b)^2 = 169 (2b + 5)^2 = 169 [URL=' (2b + 5)^2 through our search engine[/URL], and you get: 4b^2 + 20b + 25 Set this equal to 169 above: 4b^2 + 20b + 25 = 169 [URL=' that quadratic equation in our search engine[/URL], and you get: b = (-9, 4) But the problem asks for [I]positive[/I] numbers. So [B]b = 4[/B] is one of our solutions. Substitute b = 4 into equation (1) above, and we get: a - [I]b[/I] = 5 [URL=' - 4 = 5[/URL] [B]a = 9 [/B] Therefore, we have [B](a, b) = (9, 4)[/B]

The difference of 2 positive numbers is 54. The quotient obtained on dividing the 1 by the other is 4. Find the numbers. Let the numbers be x and y. We have: [LIST] [*]x - y = 54 [*]x/y = 4 [*]Cross multiply x/y = 4 to get x = 4y [*]Now substitute x = 4y into the first equation [*](4y) - y = 54 [*]3y = 54 [*]Divide each side by 3 [*][B]y = 18[/B] [*]If x = 4y, then x = 4(18) [*][B]x = 72[/B] [/LIST]

the difference of 5 and the cube of the sum of x and y The sum of x and y: x + y The cube of the sum of x and y means we raise x + y to the 3rd power: (x + y)^3 The difference of 5 and the cube of the sum of x and y [B]5 - (x + y)^3[/B]

The difference of 6 and the sum a and b The sum of a and b means we add b to a: a + b The difference of 6 and the sum of a and b: [B]6 - (a + b)[/B]

The difference of 9 and the sum of x and 4 The sum of x and 4: x + 4 The difference of 9 and the sum of x and 4: [B]9 - (x + 4)[/B]

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number? We have two expressions: [U]Expression 1: [I]The difference of a number and 6[/I][/U] The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The difference of a number and 6 means we subtract 6 from x: x - 6 [U]Expression 2: [I]5 times the sum of the number and 2[/I][/U] The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The sum of a number and 2 means we add 2 to x: x + 2 5 times the sum means we multiply x + 2 by 5 5(x + 2) [U]For the last step, we evaluate the expression [I]is the same as[/I][/U] This means equal to, so we set x - 6 equal to 5(x + 2) [B]x - 6 = 5(x + 2)[/B]

The difference of two numbers is 12 and their mean is 15. Find the two numbers. Let the two numbers be x and y. We're given: [LIST=1] [*]x - y = 12 [*](x + y)/2 = 15. <-- Mean is an average [/LIST] Rearrange equation 1 by adding y to each side: x - y + y = y + 12 Cancelling the y's on the left side, we get: x = y + 12 Now substitute this into equation 2: (y + 12 + y)/2 = 15 Cross multiply: y + 12 + y = 30 Group like terms for y: 2y + 12 = 30 [URL=' this equation into our search engine[/URL], we get: [B]y = 9[/B] Now substitute this into modified equation 1: x = y + 12 x = 9 + 12 [B]x = 21[/B]

the difference of x and y added to twice the sum of a and b Take this algebraic expression in parts: [LIST] [*]The difference of x and y: x - y [*]The sum of a and b: a + b [*]Twice the sum of a and b means we multiply a + b by 2: 2(a + b) [*]The phrase [I]added to[/I] means we add: [/LIST] [B]x - y + 2(a + b)[/B]

The difference when (10x - 6y) is subtracted from (7x - 4y) In simplest form (7x - 4y) - (10x - 6y) 7x - 4y - 10x - -6y 7x - 4y - 10x + 6y (7 - 10)x + (-4 + 6)y [B]-3x + 2y[/B]

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased by x cm and its width is increased by x cm, its area is increased by 35 sq. cm. a. Express the new length and the new width in terms of x. b. Express the new area of the rectangle in terms of x. c. Find the value of x. Calculate the current area. Using our [URL=' calculator with length = 30 and width = 18[/URL], we get: A = 540 a) Decrease length by x and increase width by x, and we get: [LIST] [*]length = [B]30 - x[/B] [*]width = [B]18 + x[/B] [/LIST] b) Our new area using the lw = A formula is: (30 - x)(18 + x) = 540 + 35 Multiplying through and simplifying, we get: 540 - 18x + 30x - x^2 = 575 [B]-x^2 + 12x + 540 = 575[/B] c) We have a quadratic equation. To solve this, [URL=' type it in our search engine, choose solve[/URL], and we get: [B]x = 5 or x = 7[/B] Trying x = 5, we get: A = (30 - 5)(18 + 5) A = 25 * 23 A = 575 Now let's try x = 7: A = (30 - 7)(18 + 7) A = 23 * 25 A = 575 They both check out. So we can have

The distance to the nearest exit door is less than 100 feet. Use d to represent the distance (in feet) to the nearest exit door. Less than means we use the < sign: [B]d < 100[/B]

The distribution of actual weights of 8 oz chocolate bars produced by a certain machine is normal with =8.1 ounces and ?=0.1 ounces. A sample of 5 of these chocolate bars is selected. What is the probability that their average weight is less than 8 ounces? Calculate Z score and probability using [URL=' calculator[/URL]: Z = -2.236 P(X < -2.236) = [B]0.012545[/B]

The domain of a relation is all even negative integers greater than -9. The range y of the relation is the set formed by adding 4 to the numbers in the domain. Write the relation as a table of values and as an equation. The domain is even negative integers greater than -9: {-8, -6, -4, -2} Add 4 to each x for the range: {-8 + 4 = -4, -6 + 4 = -2. -4 + 4 = 0, -2 + 4 = 2} For ordered pairs, we have: (-8, -4) (-6, -2) (-4, 0) (-2, 2) The equation can be written: y = x + 4 on the domain (x | x is an even number where -8 <= x <= -2)

The doubling time of a population of flies is 8 hours. a) By what factor does a population increase in 24 hours? b) By what factor does the population increase in 2 weeks? a) If the population doubles every 8 hours, then it doubles 3 times in 24 hours, since 24/8 = 3. So 2 * 3 = 6. The increase factor is [B]6[/B] b) Since a) is one full day, we now need to know how much it doubles in 14 days, which is 2 weeks. We take our factor of 6 for each day, and multiply it by 14: 14 * 6 = [B]84[/B]

The earth makes a full rotation in 24 hours. Jupiter takes approximately 58 days, 15 h, and 30 min to complete a full rotation. How many hours does it take Jupiter to complete a full rotation? Show your work using the correct conversion factors. Convert 58 days, 15 h, and 30 min to hours. [LIST=1] [*]Type [URL=' days[/URL] into the search engine to get 1,392 hours. [*]Add 15 hours to get 1,392 + 15 = 2,007 hours [*]Now convert the 30 min to hours. [URL=' 30 minutes into the search engine[/URL] to get 0.5 hours [*]Add up (1), (2), and (3) to get 1,392 + 15 + 0.5 = [B]2007.5[/B] hours for a full rotation. [/LIST]

The enrollment at High School R has been increasing by 20 students per year. High School R currently has 200 students. High School T has 400 students and is decreasing 30 students per year. When will the two school have the same enrollment of students? Set up the Enrollment function E(y) where y is the number of years. [U]High School R:[/U] [I]Increasing[/I] means we add E(y) = 200 + 20y [U]High School T:[/U] [I]Decreasing[/I] means we subtract E(y) = 400 - 30y When the two schools have the same enrollment, we set the E(y) functions equal to each other 200 + 20y = 400 - 30y To solve this equation for y, we [URL=' it in our search engine[/URL] and we get: y = [B]4[/B]

The entrance fee to the national park is $30. A campsite fee is $15 per night. Write an equation to represent the situation. Let n be the number of nights. We have a cost (C) of: C = Cost per night * n + entrance fee C = [B]15n + 50[/B]

the equation of a line is y = mx + 4. find m if the line passes through (-5,0) Plug in our numbers of x = -5, and y = 0: -5m + 4 = 0 To solve for m, we [URL=' in this equation into our search engine[/URL] and we get: [B]m = 0.8 or 4/5[/B] so our line equation becomes: [B]y = 4/5x + 4[/B]

The expression (5x - 2)/(x + 3) is equivalent to which of the following? [LIST] [*]A) (5 - 2)/3 [*]B) 5 - 2/3 [*]C) 5 - (2/(x + 3)) [*]D) 5 - (17/(x + 3)) [/LIST] Let's start with an integer x = 2. Plug that into our original expression, and we get: (5(2) - 2)(2 + 3) (10 - 2)/5 8/5 So what we do next is, take x = 2, and plug it into answer choices A-D, and see which one results in 8/5 A) 3/3 = 1 <-- Nope B) Since 5 is 15/3, we have 15/3 - 2/3 = 13/3 which is over 4, so Nope C) 5 - (2/(2 + 3)) = 5 - (2/5). Since 5 is 25/5, we have 25/5 - 2/5 = 23/5. <-- Nope D) 5 - (17/(2 + 3)) = 5 - 17/5. Since 5 is 25/5, we have 25/5 - 17/5 = 8/5 <-- YES Since 8/5 = 8/5, our answer is [B]D) 5 - (17/(x + 3))[/B]

The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The second plan had a $21 monthly fee and charges an additional $.10 for each minute of calls. For how many minutes of calls will the cost of the two plans be equal? Set up the cost equation C(m) for the first plan, where m is the amount of minutes you use C(m) = 0.14m + 14 Set up the cost equation C(m) for the second plan, where m is the amount of minutes you use C(m) = 0.10m + 21 Set them equal to each other: 0.14m + 14 = 0.10m + 21 [URL=' this equation into our search engine[/URL], we get: m = [B]175[/B]

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 231 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Digit, Probability 1, 0.301 2, 0.176 3, 0.125 4, 0.097 5, 0.079 6, 0.067 7, 0.058 8, 0.051 9, 0.046 [B][U]Fradulent Checks[/U][/B] Digit, Frequency 1, 36 2, 32 3, 45 4, 20 5, 24 6, 36 7, 15 8, 16 9, 7 Complete parts (a) and (b). (a) Using the level of significance α = 0.05, test whether the first digits in the allegedly fraudulent checks obey Benford's Law. Do the first digits obey the Benford's Law?Yes or No Based on the results of part (a), could one think that the employe is guilty of embezzlement? Yes or No Show frequency percentages Digit Fraud Probability Benford Probability 1 0.156 0.301 2 0.139 0.176 3 0.195 0.125 4 0.087 0.097 5 0.104 0.079 6 0.156 0.067 7 0.065 0.058 8 0.069 0.051 9 0.03 0.046 Take the difference between the 2 values, divide it by the Benford's Value. Sum up the squares to get the Test Stat of 2.725281277 Critical Value Excel: =CHIINV(0.95,8) = 2.733 Since test stat is less than critical value, we cannot reject, so [B]YES[/B], it does obey Benford's Law and [B]NO[/B], there is not enough evidence to suggest the employee is guilty of embezzlement.

The fixed costs to produce a certain product are 15,000 and the variable costs are $12.00 per item. The revenue for a certain product is $27.00 each. If the company sells x products, then what is the revenue equation? R(x) = Revenue per item x number of products sold [B]R(x) = 27x[/B]

The flu is starting to hit Lanberry. Currently, there are 894 people infected, and that number is growing at a rate of 5% per day. Overall, how many people will have gotten the flu in 5 days? Our exponential equation for the Flu at day (d) is: F(d) = Initial Flu cases * (1 + growth rate)^d Plugging in d = 5, growth rate of 5% or 0.05, and initial flu cases of 894 we have: F(5) = 894 * (1 + 0.05)^5 F(5) = 894 * (1.05)^5 F(5) = 894 * 1.2762815625 F(5) = [B]1141[/B]

The fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the fraction? We're given two equations with a fraction with numerator (n) and denominator (d): [LIST=1] [*]n + d = 40 [*]n/d = 3/5 [/LIST] Cross multiply equation 2, we get: 5n = 3d Divide each side by 5: 5n/5 = 3d/5 n = 3d/5 Substitute this into equation 1: 3d/5 + d = 40 Multiply through both sides of the equation by 5: 5(3d/5) = 5d = 40 * 5 3d + 5d =200 To solve this equation for d, we [URL=' it in our search engine and we get[/URL]: d = [B]25 [/B] Now substitute that back into equation 1: n + 25 = 40 Using [URL=' equation solver again[/URL], we get: n = [B]15[/B]

the fuel tank of a jet used gas at a constant rate of 300 gallons for each hour of flight. the tank can hold a maximum of 2400 gallons of gas. write an equation representing the amount of fuel left in the tank as a function of the number of hours spent flying. We have an equation F(h) where h is the number of hours since the flight took off: [B]F(h) = 2400 - 300h[/B]

The function f(x) = e^x(x - 3) has a critical point at x = The critical point is where the derivative equals 0. We multiply through for f(x) to get: f(x) = xe^x - 3e^x Using the product rule on the first term f'g + fg', we get: f'(x) = xe^x + e^x - 3e^x f'(x) = xe^x -2e^x f'(x) = e^x(x - 2) We want f'(x) = 0 e^x(x - 2) = 0 When [B]x = 2[/B], then f'(x) = 0

The function f(x) = x^3 - 48x has a local minimum at x = and a local maximum at x = ? f'(x) = 3x^2 - 48 Set this equal to 0: 3x^2 - 48 = 0 Add 48 to each side: 3x^2 = 48 Divide each side by 3: x^2 = 16 Therefore, x = -4, 4 Test f(4) f(4) = 4^3 - 48(4) f(4) = 64 - 192 f(4) = [B]-128 <-- Local minimum[/B] Test f(-4) f(-4) = -4^3 - 48(-4) f(-4) = -64 + 192 f(-4) = [B]128 <-- Local maximum[/B]

The function P(x) = -30x^2 + 360x + 785 models the profit, P(x), earned by a theatre owner on the basis of a ticket price, x. Both the profit and the ticket price are in dollars. What is the maximum profit, and how much should the tickets cost? Take the [URL=' of the profit function[/URL]: P'(x) = -60x + 360 We find the maximum when we set the profit derivative equal to 0 -60x + 360 = 0 Subtract 360 from both sides: -60x = -360 Divide each side by -60 [B]x = 6 <-- This is the ticket price to maximize profit[/B] Substitute x = 6 into the profit equation: P(6) = -30(6)^2 + 360(6) + 785 P(6) = -1080 + 2160 + 785 [B]P(6) = 1865[/B]

The girls hockey team won 6 games, lost 3 games, and tied 2 games. What fraction of games did they win? Win Fraction = Won Games / Total Games Played Win Fraction = 6 / (6 + 3 + 2) Win Fraction = [B]6/11[/B]

The graph of a polynomial f(x) = (2x - 3)(x - 4)(x + 3) has x-intercepts at 3 values. What are they? A few things to note: [LIST] [*]X-intercepts are found when y (or f(x)) is 0. [*]On the right side, we have 3 monomials. [*]Therefore, y or f(x) could be 0 when [U]any[/U] of these monomials is 0 [/LIST] The 3 monomials are: [LIST=1] [*]2x - 3 = 0 [*]x - 4 = 0 [*]x + 3 = 0 [/LIST] Find all 3 x-intercepts: [LIST=1] [*]2x - 3 = 0. [URL=' our equation calculator[/URL], we see that x = [B]3/2 or 1.5[/B] [*]x - 4 = 0 [URL=' our equation calculator[/URL], we see that x = [B]4[/B] [*]x + 3 = 0 [URL=' our equation calculator[/URL], we see that x = [B]-3[/B] [/LIST] So our 3 x-intercepts are: x = [B]{-3, 3/2, 4}[/B]

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 months. Interpret the RATE OF CHANGE of the graph. [IMG] Looking at our graph, we have a straight line. For straight lines, rate of change [U][I]equals[/I][/U] slope. Looking at a few points, we have: (0, 20), (12, 30) Using our [URL=' calculator for these 2 points[/URL], we get a slope (rate of change) of: [B]5/6[/B]

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +300. Find the average velocity of the object during the first 3 seconds? (b) Use the Mean value Theorem to verify that at some time during the first 3 seconds of the fall the instantaneous velocity equals the average velocity. Find that time. Average Velocity: [ f(3) - f(0) ] / ( 3 - 0 ) Calculate f(3): f(3) = -4.9(3^2) + 300 f(3) = -4.9(9) + 300 f(3) = -44.1 + 300 f(3) = 255.9 Calculate f(0): f(0) = -4.9(0^2) + 300 f(0) = 0 + 300 f(0) = 300 So we have average velocity: Average velocity = (255.9 - 300)/(3 - 0) Average velocity = -44.1/3 Average velocity = -[B]14.7 [/B] Velocity is the first derivative of position s(t)=-4.9t^2 +300 s'(t) = -9.8t So we set velocity equal to average velocity: -9.8t = -14.7 Divide each side by -9.8 to solve for t, we get [B]t = 1.5[/B]

The hourly wages of employees at Rowan have a mean wage rate of $10 per hour with a standard deviation of $1.20. What is the probability the mean hourly wage of a random sample of 36 employees will be larger than $10.50? Assume the company has a total of 1,000 employees Using our [URL=' distribution calculator[/URL], we get P(x > 10.5) = [B]0.00621[/B]

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a) What is the probability that a randomly person has an IQ between 85 and 115? b) Find the 90th percentile of the IQ distribution c) If a random sample of 100 people is selected, what is the standard deviation of the sample mean? a) [B]68%[/B] from the [URL=' rule calculator[/URL] b) P(z) = 0.90. so z = 1.28152 using Excel NORMSINV(0.9)(X - 100)/10 = 1.21852 X = [B]113[/B] rounded up c) Sample standard deviation is the population standard deviation divided by the square root of the sample size 15/sqrt(100) = 15/10 =[B] 1.5[/B]

The Lakers recently scored 81 points. Their points came from 2 and 3 point baskets. If they made 39 baskets total, how many of each basket did they make? Let x = 2 point baskets and y = 3 point baskets. We have the following given equations: [LIST=1] [*]x + y = 39 [*]2x + 3y = 81 [/LIST] Using our [URL=' equations calculator[/URL], we get: [B]x = 36 <-- 2 point baskets y = 3 <-- 3[B] point baskets [/B][/B] To confirm our work: [LIST=1] [*]36 + 3 = 39 [*]2(36) + 3(3) = 72 + 9 = 81 [/LIST]

The length of a rectangle is 6 less than twice the width. If the perimeter is 60 inches, what are the dimensions? Set up 2 equations given P = 2l + 2w: [LIST=1] [*]l = 2w - 6 [*]2l + 2w = 60 [/LIST] Substitute (1) into (2) for l: 2(2w - 6) + 2w = 60 4w - 12 + 2w = 60 6w - 12 = 60 To solve for w, [URL=' this into our math solver [/URL]and we get: w = [B]12 [/B] To solve for l, substitute w = 12 into (1) l = 2(12) - 6 l = 24 - 6 l = [B]18[/B]

The length of a rectangle is equal to triple the width. Find the length of the rectangle if the perimeter is 80 inches. The perimeter (P) of a rectangle is: 2l + 2w = P We're given two equations: [LIST=1] [*]l = 3w [*]2l + 2w = 80 [/LIST] We substitute equation 1 into equation 2 for l: 2(3w) + 2w = 80 6w + 2w = 80 To solve this equation for w, we [URL=' it in our search engine[/URL] and we get: w = 10 To solve for the length (l), we substitute w = 10 into equation 1 above: l = 3(10) l = [B]30[/B]

The length of a rectangle is three times its width.If the perimeter is 80 feet, what are the dimensions? We're given 2 equations: [LIST=1] [*]l = 3w [*]P = 80 = 2l + 2w = 80 [/LIST] Substitute (1) into (2) for l: 2(3w) + 2w = 80 6w + 2w = 80 8w = 80 Divide each side by 8: 8w/8 = 80/8 w = [B]10 [/B] Substitute w = 10 into (1) l = 3(10) l = [B]30[/B]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building. P = 2l + 2w Since P = 120, we have: (1) 2l + 2w = 120 We are also given: (2) l = 3w - 6 Substitute equation (2) into equation (1) 2(3w - 6) + 2w = 120 Multiply through: 6w - 12 + 2w = 120 Combine like terms: 8w - 12 = 120 Add 12 to each side: 8w = 132 Divide each side by 8 to isolate w: w =16.5 Now substitute w into equation (2) l = 3(16.5) - 6 l = 49.5 - 6 l = 43.5 So (l, w) = (43.5, 16.5)

The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft The frame is a rectangle. The area of a rectangle is A = lw. So were given: [LIST=1] [*]l = w + 1 [*]lw = 12 [/LIST] Substitute equation (1) into equation (2) for l: (w + 1) * w = 12 Multiply through and simplify: w^2 + w = 12 We have a quadratic equation. To solve for w, we type this equation into our search engine and we get two solutions: w = 3 w = -4 Since width cannot be negative, we choose the positive result and have: w = [B]3[/B] To solve for length, we plug w = 3 into equation (1) above and get: l = 3 + 1 l = [B]4[/B]

The length of Sallys garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. Find the dimensions of Sallys garden. Gardens have a rectangle shape. Perimeter of a rectangle is 2l + 2w. We're given: [LIST=1] [*]l = 3w + 4 [I](3 times the width Plus 4 since greater means add)[/I] [*]2l + 2w = 72 [/LIST] We substitute equation (1) into equation (2) for l: 2(3w + 4) + 2w = 72 Multiply through and simplify: 6w + 8 + 2w = 72 (6 +2)w + 8 = 72 8w + 8 = 72 To solve this equation for w, we [URL=' it in our search engine[/URL] and we get: w = [B]8 [/B] To solve for l, we substitute w = 8 above into Equation (1): l = 3(8) + 4 l = 24 + 4 l = [B]28[/B]

The length of Sallys garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters A garden is a rectangle, which has perimeter P of: P = 2l + 2w With P = 72, we have: 2l + 2w = 72 We're also given: l = 3w + 4 We substitute this into the perimeter equation for l: 2(3w + 4) + 2w = 72 6w + 8 + 2w = 72 To solve this equation for w, we t[URL=' it in our search engine[/URL] and we get: w =[B] 8[/B] Now, to solve for l, we substitute w = 8 into our length equation above: l = 3(8) + 4 l = 24 + 4 l = [B]28[/B]

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length and width. A flag is a rectangle shape. So we have the following equations Since P = 2l + 2w, we have 2l + 2w = 60 l = 7w - 2 Substitute Equation 1 into Equation 2: 2(7w -2) + 2w = 60 14w - 4 + 2w = 60 16w - 4 = 60 Add 4 to each side 16w = 64 Divide each side by 16 to isolate w w = 4 Which means l = 7(4) - 2 = 28 - 2 = 26

The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a letter that is not A? ALGEBRA has 7 letters Of the 7 letters, we have 2 A's. So we have 7 - 2 = 5 letters which are not A P(Not A) = Letters not A / Total letters P(Not A) = [B]5/7[/B]

The margarita is one of the most common tequila-based cocktails, made with tequila, triple sec, and lime juice, often served with salt on the glass rim. A manager at a local bar is concerned that the bartender is not using the correct amounts of the three ingredients in more than 50% of margaritas. He secretly observed the bartender and found that he used the CORRECT amounts in only 9 out of the 39 margaritas in the sample. Use the critical value approach to test if the manager's suspicion is justified at ? = 0.10. Let p represent the proportion of all margaritas made by the bartender that have INCORRECT amounts of the three ingredients. Use Table 1. a. Select the null and the alternative hypotheses. [B]H0: p ? 0.50; HA: p > 0.50[/B] [B][/B] b. Calculate the sample proportion. (Round your answer to 3 decimal places.) 9/39 = [B]0.231 [/B] c. Calculate the value of test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.) Using our [URL=' hypothesis calculator[/URL], we get: [B]Test Stat = -3.36[/B] [B][/B] d. Calculate the critical value. (Round your answer to 2 decimal places.) Using the link above, we get a critical value of [B]1.2816 [/B] e. What is the conclusion? [B]The managers suspicion is not justified since the value of the test statistic does not fall in the rejection region. Do not reject H0[/B] [B][/B]

The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 years old. What is the mean age (nearest year) of all the people in the office? Mean is another word for [U]average[/U]. Mean age of women = Sum of all ages women / number of women We're told mean age of women is 30, so we have: Sum of all ages women / 10 = 30 Cross multiply, and we get: Sum of all ages of women = 30 * 10 Sum of all ages of women = 300 Mean age of men = Sum of all ages men / number of men We're told mean age of men is 29, so we have: Sum of all ages men / 10 = 29 Cross multiply, and we get: Sum of all ages of men = 29 * 10 Sum of all ages of men = 290 [U]Calculate mean age (nearest year) of all the people in the office:[/U] mean age of all the people in the office = Sum of all ages of people in the office (men and women) / Total number of people in the office mean age of all the people in the office = (300 + 290) / (10 + 10) mean age of all the people in the office = 590 / 20 mean age of all the people in the office = 29.5 The question asks for nearest year. Since this is a decimal, we round down to either 29 or up to 30. Because the decimal is greater or equal to 0.5 (halfway), we round [U]up[/U] to [B]30[/B]

The mean age of 5 people in a room is 28 years. A person enters the room. The mean age is now 32. What is the age of the person who entered the room? The sum of the 5 people's scores is S. We know: S/5 = 28 Cross multiply: S = 140 We're told that: (140 + a)/6 = 32 Cross multiply: 140 + a = 192 [URL=' this equation into our search engine[/URL], we get: a = [B]52[/B]

The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. What is the age of the person who entered the room? Mean = Sum of Ages in Years / Number of People 32 = Sum of Ages in Years / 5 Cross multiply: Sum of Ages in Years = 32 * 5 Sum of Ages in Years = 160 Calculate new mean after the next person enters the room. New Mean = (Sum of Ages in Years + New person's age) / (5 + 1) Given a new Mean of 40, we have: 40 = (160 + New person's age) / 6 Cross multiply: New Person's Age + 160 = 40 * 6 New Person's Age + 160 = 240 Let the new person's age be n. We have: n + 160 = 240 To solve for n, [URL=' type this equation into our search engine[/URL] and we get: n = [B]80[/B]

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. What is the age of the person who entered the room? The mean formulas is denoted as: Mean = Sum of Ages / Total People We're given Mean = 38 and Total People = 5, so we plug in our numbers: 28 = Sum of Ages / 5 Cross multiply, and we get: Sum of Ages = 28 * 5 Sum of Ages = 140 One more person enters the room. The mean age is now 39. Set up our Mean formula: Mean = Sum of Ages / Total People With a new Mean of 39 and (5 + 1) = 6 people, we have: 39 = Sum of Ages / 6 But the new sum of Ages is the old sum of ages for 5 people plus the new age (a): Sum of Ages = 140 + a So we have: 29 = (140 + a)/6 Cross multiply: 140 + a = 29 * 6 140 + a = 174 To solve for a, [URL=' type this equation into our search engine[/URL] and we get: a = [B]34[/B]

The mean of 3 numbers is 20. Two of the numbers are 21, and 35. What is the 3rd number? The mean of 3 numbers is the sum of 3 numbers divided by 3. Let the 3rd number be n. We have: Mean = (21 + 35 + n) / 3 The Mean is given as 20, so we have: 20 = (n + 56) / 3 Cross multiply: n + 56 = 20 * 3 n + 56 = 60 To solve for n, we [URL=' this number in our search engine [/URL]and we get: n = [B]4[/B]

The mean of two numbers is 49.1. The first number is 18.3. What is the second number We call the second number n. Since the mean is an average, in this case 2 numbers, we have: (18.3 + n)/2 = 49.1 Cross multiply: 18.3 + n = 98.2 [URL=' this equation into our search engine[/URL], we get: [B]n = 79.9[/B]

the midpoint between m and n The [I]midpoint is halfway between[/I] m and n: [B](m + n)/2[/B]

The negative of the sum of C and D is equal to the difference of the negative of C and D The negative of the sum of C and D means -1 times the sum of C and D -(C + D) Distribute the negative sign: -C - D the difference of the negative of C and D means we subtract D from negative C -C - D So this statement is [B]true[/B] since -C - D = -C - D

The next number in the series 2,5,11,20,32,47, is [LIST] [*]2 + 3 = 5 [*]5 + 6 = 11 [*]11 + 9 = 20 [*]20 + 12 = 32 [*]32 + 15 = 47 [/LIST] Notice the addition pattern: 3, 6, 9, 12, 15 This means our next term is: 47 + (15 + 3) 47 + 18 [B]65 [MEDIA=youtube]mAj3tqXUbZs[/MEDIA][/B]

The Oakdale High School Speech and Debate Club hosted its annual car wash fundraiser. Each club member brought a bottle of car wash soap, so there were 8 total bottles. 6 of the bottles contained orange soap. If a club member randomly selects 5 bottles to pour into the first soap bucket, what is the probability that all of them contain orange soap? This is assumed to be draw without replacement, so we have: [LIST=1] [*]Draw 1: 6/8 [*]Draw 2: 5/7 [*]Draw 3: 4/6 [*]Draw 4: 3/5 [*]Draw 5: 2/4 [/LIST] Since they are independent events, we multiply: 6/8 * 5/7 * 4/6 * 3/5 * 2/4 (6 * 5 * 4 * 3 * 2)/(8 * 7 * 6 * 5 * 4) 720/6720 [B]0.1071[/B]

The opposite of the difference of h and 5 The difference of h and 5 h - 5 The opposite of the difference of h and 5 means we multiply the difference of h and 5 by -1: -(h - 5) Distribute the negative sign: [B]5 - h[/B]

The ordered pairs (8,12), (16, 24), (x, 21), (26, y ) represent a proportional relationship. Find the value of x and the value of y. 12/8 = 1.5 24/16 = 1.5 So we have our proportion; y/x = 1.5 or 3/2 [U]For (x, 21), we have:[/U] 21/x = 3/2 [URL=' this proportion into our search engine[/URL] and we get: x = [B]14[/B] For (26, y), we have: y/26 = 3/2 [URL=' this proportion into our search engine[/URL] and we get; y = [B]39[/B]

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days. What is the median recovery time? a. 2.7 b. 5.3 c. 7.4 d. 2.1 [B]b. 5.3 (mean, median, and mode are all the same in a normal distribution)[/B]

The perimeter of a college basketball court is 102 meters and the length is twice as long as the width. What are the length and width? A basketball court is a rectangle. The perimeter P is: P = 2l + 2w We're also given l = 2w and P = 102. Plug these into the perimeter formula: 2(2w) + 2w = 102 4w + 2w = 102 6w = 102 [URL=' this equation into our calculator[/URL], we get: [B]w = 17[/B] Plug this into the l = 2w formula, we get: l = 2(17) [B]l = 34[/B]

The perimeter of a garden is 70 meters. Find its actual dimensions if its length is 5 meters longer than twice its width. Let w be the width, and l be the length. We have: P = l + w. Since P = 70, we have: [LIST=1] [*]l + w = 70 [*]l = 2w + 5 [/LIST] Plug (2) into (1) 2w + 5 + w = 70 Group like terms: 3w + 5 = 70 Using our [URL=' calculator[/URL], we get [B]w = 21.66667[/B]. Which means length is: l = 2(21.6667) + 5 l = 43.33333 + 5 [B]l = 48.3333[/B]

The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it? [U]Assumptions and givens:[/U] [LIST] [*]The poster has a rectangle shape [*]l = 6 [*]P = 20 [*]The perimeter of a rectangle (P) is: 2l + 2w = P [/LIST] Plugging in our l and P values, we get: 2(6) + 2w = 20 Multiplying through and simplifying, we get: 12 + 2w = 20 To solve for w, we [URL=' this equation into our search engine [/URL]and we get: w = [B]4[/B]

The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Find the length and the width of the rectangle. l = 4w - 15 Perimeter = 2l + 2w Substitute, we get: 400 = 2(4w - 15) + 2w 400 = 8w - 30 + 2w 10w - 30 = 400 Add 30 to each side 10w = 370 Divide each side by 10 to isolate w w = 37 Plug that back into our original equation to find l l = 4(37) - 15 l = 148 - 15 l = 133 So we have (l, w) = (37, 133)

The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is its width? The formula for a rectangles perimeter P, is: P = 2l + 2w where l is the length and w is the width. Plugging in our P = 340 and l = 97, we have: 2(97) + 2w = 340 Multiply through, we get: 2w + 194 = 340 [URL=' this equation into our search engine[/URL], we get: [B]w = 73[/B]

The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it? Set up the perimeter equation: 2l + 2w = P Given P = 204 and l = 66, we have: 2(66) + 2w = 204 2w + 132 = 204 Using our [URL=' solver,[/URL] we get w = [B]36[/B].

The perimeter of a rectangular field is 220 yd. the length is 30 yd longer than the width. Find the dimensions We are given the following equations: [LIST=1] [*]220 = 2l + 2w [*]l = w + 30 [/LIST] Plug (1) into (2) 2(w + 30) + 2w = 220 2w + 60 + 2w = 220 Combine like terms: 4w + 60 = 220 [URL=' 4w + 60 = 220 into the search engine[/URL], and we get [B]w = 40[/B]. Now plug w = 40 into equation (2) l = 40 + 30 [B]l = 70[/B]

The perimeter of a rectangular field is 250 yards. If the length of the field is 69 yards, what is its width? Set up the rectangle perimeter equation: P = 2l + 2w For l = 69 and P = 250, we have: 250= 2(69) + 2w 250 = 138 + 2w Using our [URL=' solver[/URL], we get: [B]w = 56 [/B]

The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is its length? Set up the perimeter (P) of a rectangle equation given length (l) and width (w): 2l + 2w = P We're given P = 300 and w = 59. Plug these into the perimeter equation: 2l + 2(59) = 300 2l + 118 = 300 [URL=' this equation into our search engine[/URL], we get: [B]l = 91[/B]

The perimeter of a rectangular notecard is 16 inches. The notecard is 5 inches wide. How tall is it? Perimeter of a rectangle P is: P = 2l + 2w We have: 2l + 2w = 16 We are given w = 5, so we have: 2l + 2(5) = 16 2l + 10 = 16 [URL=' this into our equation calculator[/URL], we get [B]l = 3[/B].

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. What are the dimensions of the patio? Perimeter of a rectangle is: P = 2l + 2w We're given l = w + 3 and P = 54. So plug this into our perimeter formula: 54= 2(w + 3) + 2w 54 = 2w + 6 + 2w Combine like terms: 4w + 6 = 54 [URL=' this equation into our search engine[/URL], we get: [B]w = 12[/B] Plug this into our l = w + 3 formula: l = 12 + 3 [B]l = 15[/B]

The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, what is its width? The perimeter for a rectangle (P) is given as: 2l + 2w = P We're given P = 258 and l = 71. Plug these values in: 2(71) + 2w = 258 142 + 2w = 258 [URL=' this equation into our search engine[/URL], we get: [B]w = 58[/B]

The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it? The perimeter for a rectangle is given below: P = 2l + 2w We're given l = 7 and P = 60. Plug this into the perimeter formula: 60 = 2(7) + 2w 60 = 14 + 2w Rewritten, it's 2w + 14 = 60. [URL=' this equation into our search engine[/URL], we get [B]w = 23[/B].

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000. [LIST] [*]h = b + 70 [*]A = 1/2bh = 3000 [/LIST] Substitute the height equation into the area equation 1/2b(b + 70) = 3000 Multiply each side by 2 b^2 + 70b = 6000 Subtract 6000 from each side: b^2 + 70b - 6000 = 0 Using our [URL=' calculator[/URL], we get: b = 50 and b = -120 Since the base cannot be negative, we use b = 50. If b = 50, then h = 50 + 70 = 120 The perimeter is b + h + hypotenuse Using the [URL=' calculator[/URL], we get hypotenuse = 86.02 Adding up all 3 for the perimeter: 50 + 70 + 86.02 = [B]206.02[/B]

The plumber added an extra $35 to her bill what is the algebraic phrase Added $35 to a bill (b) is: [B]b + 35[/B]

The point (1,5) is a solution to the equation 2y - x = 9 [B]Yes[/B], because: 2(5) - 1 ? 9 10 - 1 ? 9 9 = 9

The points -5, -24 and 5,r lie on a line with slope 4. Find the missing coordinate r. Slope = (y2 - y1)/(x2 - x1) Plugging in our numbers, we get: 4 = (r - -24)/(5 - -5) 4 = (r +24)/10 Cross multiply: r + 24 = 40 Subtract 24 from each side: [B]r = 16[/B]

The points 6,4 and 9,r lie on a line with slope 3. Find the missing coordinate r. Slope = (y2 - y1)/(x2 - x1) Plugging in our numbers, we get: 3 = (r - 4)/(9 - 6) 3 = (r - 4)/3 Cross multiply: r - 4 = 9 Add 4 to each side: [B]r = 13[/B]

The polynomial function P(x) = 75x - 87,000 models the relationship between the number of computer briefcases x that a company sells and the profit the company makes, P(x). Find P (4000), the profit from selling 4000 computer briefcases. Plug in 4,000 for x: P(4000) = 75(4000) - 87,000 P(4000) = 300,000- 87,000 P(4000) = [B]213,000[/B]

The population of goats on a particular nature reserve t years after the initial population was settled is modeled by p(t) = 4000 - 3000e^-0.2t. How many goats were initially present? [U]Initially present means at time 0. Substituting t = 0, p(0), we get:[/U] p(0) = 4000 - 3000e^-0.2(0) p(0) = 4000 - 3000e^0 p(0) = 4000 - 3000(1) p(0) = 4000 - 3000 [B]p(0) = 1000[/B]

The price of a cheap backpack is $15 less than an expensive backpack. When Emily bought both, she paid $75. What is the cost of the cheap backpack? backpack cost = b Cheap backpack = b - 15 The total of both items equals 75: b + b - 15 = 75 Solve for [I]b[/I] in the equation b + b - 15 = 75 [SIZE=5][B]Step 1: Group the b terms on the left hand side:[/B][/SIZE] (1 + 1)b = 2b [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2b - 15 = + 75 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -15 and 75. To do that, we add 15 to both sides 2b - 15 + 15 = 75 + 15 [SIZE=5][B]Step 4: Cancel 15 on the left side:[/B][/SIZE] 2b = 90 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2b/2 = 90/2 b = 45 Cheap backpack = 45 - 15 = [B]30 [URL='

the price of a remote control helicopter is $34.40. a remote control boat costs 4/5 the price of the helicopter. sales tax on the remote control boat is 8%.what is the price of the remote control boat, including sales tax? round your answer to the nearest penny 4/5 of 34.40 = $27.52 Add sales tax: 27.52(1.08) = [B]$29.72[/B]

The price p of a gyms membership is $30 for an enrollment fee and $12 per week w to be a member. What is the cost to be a member for 5 weeks? Set up the cost function C(w) C(w) = 12w + 30 The problem asks for C(5) C(5) = 12(5) + 30 C(5) = 60 + 30 C(5) = [B]90[/B]

the product of 2 less than a number and 7 is 13 Take this algebraic expression in [U]4 parts[/U]: Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x Part 2 - 2 less than a number means we subtract 2 from x x - 2 Part 3 - The phrase [I]product[/I] means we multiply x - 2 by 7 7(x - 2) Part 4 - The phrase [I]is[/I] means an equation, so we set 7(x - 2) equal to 13 [B]7(x - 2) = 13[/B]

the product of 3 and the sum of m and 2n The sum of m and 2n means we add 2n to m: m + 2n The product of 3 means we multiply the sum m + 2n by 3: [B]3(m + 2n)[/B]

the product of 8 and 15 more than a number. Take this algebraic expression in pieces. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 15 more than x means we add 15 to x: x + 15 The product of 8 and 15 more than a number means we multiply 8 by x + 15 [B]8(x + 15)[/B]

Let the number be x. Let the square be x^2. So we have (x)(x^2) = x^3 < 8 Take the cube root of this, we get x = 2

The product of two consecutive integers is greater than 100 Take an integer x. Next consecutive integer is x + 1 The product of those integers is: x(x + 1) This product is greater than 100 which gives us the algebraic expression of: x(x + 1) > 100 IF we want to solve for x: x^2 + x > 100 Subtract 100 from each side: x^2 + x - 100 > 0 [URL=' this quadratic:[/URL]

The product of two positive numbers is 96. Determine the two numbers if one is 4 more than the other. Let the 2 numbers be x and y. We have: [LIST=1] [*]xy = 96 [*]x = y - 4 [/LIST] [U]Substitute (2) into (1)[/U] (y - 4)y = 96 y^2 - 4y = 96 [U]Subtract 96 from both sides:[/U] y^2 - 4y - 96 = 0 [U]Factoring using our quadratic calculator, we get:[/U] (y - 12)(y + 8) So y = 12 and y = -8. Since the problem states positive numbers, we use [B]y = 12[/B]. Substituting y = 12 into (2), we get: x = 12 - 4 [B]x = 8[/B] [B]We have (x, y) = (8, 12)[/B]

The quantity x minus y divided by 4 The quantity x minus y x - y The quantity x minus y divided by 4 [B](x - y)/4[/B]

The quotient of 2 and the sum of a number and 1. The phrase [I]a number[/I] represents an arbitrary variable, let's call it x. The sum of a number and 1 is written as: x + 1 The word [I]quotient[/I] means a fraction. So we divide 2 by x + 1 2 -------- ( x + 1)

the quotient of 3 and u is equal to 52 divided by u Take this algebraic expression in 3 parts: [LIST=1] [*]The quotient of 3 and u means we divide 3 by u: 3/u [*]52 divided by u means we divide 52 by u: 52/u [*]The phrase [I]is equal to[/I] means an equation, so we set (1) equal to (2) [/LIST] [B]3/u = 52/u[/B]

The quotient of 3 plus y and 12 minus x 3 plus y: 3 + y 12 minus x 12 - x The quotient of 3 plus y and 12 minus x: [B](3 + y)/(12 - x)[/B]

the quotient of 4 more than a number and 7 is 10 Take this algebraic expression in pieces: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 4 more than a number means we add 4 to x: x + 4 The quotient of 4 more than a number and 7 means we divide x + 4 by 7 (x + 4)/7 The word [I]is[/I] means an equation, so we set (x + 4)/7 equal to 10 [B](x + 4)/7 = 10[/B]

the quotient of 7 and the total of 5 and x The total of 5 and x 5 + x the quotient of 7 and the total of 5 and x [B]7/(5 + x)[/B]

The quotient of 9-x and twice x Twice x means we multiply x by 2: 2x The quotient of 9 - x and twice x is formed by the fraction: [B](9 - x)/2x[/B]

the quotient of m and the sum of n and p. The sum of n and p means we add p to n: n + p The quotient means a fraction, so we divide m by (n + p) [B]m/(n + p)[/B]

The quotient of the quantity of x plus y and 3 Quantity x plus y x + y Quotient of this and 3 [B](x + y)/3[/B]

the quotient of the sum and difference of c and d The sum of c and d: c + d The difference of c and d: c - d the quotient of the sum and difference of c and d [B](c + d)/(c - d)[/B]

The ratio between the sum of a and b and the difference of a and b is equal to 5. The sum of a and b: a + b The difference of a and b: a - b The ratio between the sum of a and b and the difference of a and b (a + b)/(a - b) The ratio between the sum of a and b and the difference of a and b is equal to 5. [B](a + b)/(a - b) = 5[/B]

The ratio of the measures of the 3 angles of a triangle is 1:2:3. What is the measure of the largest angle in degrees? Let the smallest angle be x. Then we have 3 angles based on the ratio: x, 2x, 3x We know the sum of the angles of a triangle equals 180. So we have: x + 2x + 3x = 180 6x = 180 Divide each side by 6: 6x/6 = 180/6 x = 30 The largest angle is 3(30) = [B]90 [MEDIA=youtube]l8Lc6YtK9dg[/MEDIA][/B]

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk [I]m[/I] and cups of juice [I]j[/I] a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone? Total calcium = Milk calcium + Juice Calcium Calculate Milk Calcium: Milk Calcium = 299m where m is the number of cups of milk Calculate Juice Calcium: Juice Calcium = 261j where j is the number of cups of juice The phrase [I]meet or exceed[/I] means greater than or equal to, so we have an inequality, where Total Calcium is greater than or equal to 1000. So we write our inequality as: Milk calcium + Juice Calcium >= Total Calcium [B]299m + 261j >= 1000[/B]

The regular price for a television is Q dollars. Each Saturday televisions are 20% off (The discount is .2Q). What is the price of a television on Saturday in terms of Q? Q = Regular Price .2Q = Discount Discounted Price = Q - .2Q = [B]0.8Q[/B]

The relief time provided by a standard dose of a popular childrens allergy medicine averages 7.9 hours with a standard deviation of 2.2 hours. Use Table 1. a. Determine the percentage of children who experience relief for less than 6.4 hours if the relief time follows a normal distribution. (Round your answer to 2 decimal places.) Using our [URL=' distribution calculator[/URL], we get Answer = [B]0.25[/B]

The rent for an apartment is $6600 per year and increases at a rate of 4% each year. Find the rent of the apartment after 5 years. Round your answer to the nearest penny. Our Rent R(y) where y is the number of years since now is: R(y) = 6600 * (1.04)^y <-- Since 4% is 0.04 The problem asks for R(5): R(5) = 6600 * (1.04)^5 R(5) = 6600 * 1.2166529024 R(5) = [B]8,029.91[/B]

The revenue for selling x candles is given by f(x)=12x. The teams profit is $40 less than 80% of the revenue of selling x candles. write a function g to model the profit. Profit = Revenue - Cost We are given the revenue function f(x) = 12x. We are told the profit is 0.8(Revenue) - 40. Our profit function P(x) is: P(x) = 0.8(12x) - 40 Simplifying, we have: [B]P(x) = 9.6x - 40[/B]

The sales price s of a pair of shoes plus 4% sales tax Total price is s(1 + 0.04) or [B]s(1.04)[/B]

The sales tax rate in a city is 7.27%. How much sales tax is charged on a purchase of 5 headphones at $47.44 each? What is the total price? [U]First, calculate the pre-tax price:[/U] Pre-tax price = Price per headphone * Number of Headphones Pre-tax price = $47.44 * 5 Pre-tax price = $237.20 Now calculate the tax amount: Tax Amount = Pre-Tax Price * (Tax Rate / 100) Tax Amount = $237.20 * 7.27/100 Tax Amount = $237.20 * 0.0727 Tax Amount = [B]$17.24 [/B] Calculate the total price: Total Price = Pre-Tax price + Tax Amount Total Price = $237.20 + $17.24 Total Price = [B]$254.44[/B]

The scale of a map shows that 1/2 inch is equal to 3/4 of a mile. How many inches on a map would be equal to 3 miles? Set up a proportion of scale to actual distance 1/2 / 3/4 = x/3 4/3 = x/3 Cross multiply: 3x = 12 Divide each side by 3: 3x/3 = 12/3 x = [B]4 (1/2 inch sections) or 2 inches[/B]

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for $40. Write a cost and revenue function and determine the break-even point. [U]Calculate cost function C(b) with b as the number of books:[/U] C(b) = Cost per book * b + Overhead [B]C(b) = 15b + 5500[/B] [U]Calculate Revenue Function R(b) with b as the number of books:[/U] R(b) = Sales Price per book * b [B]R(b) = 40b[/B] [U]Calculate break even function E(b):[/U] Break-even Point = Revenue - Cost Break-even Point = R(b) - C(b) Break-even Point = 40b - 15b - 5500 Break-even Point = 25b - 5500 [U]Calculate break even point:[/U] Break-even point is where E(b) = 0. So we set 25b - 5500 equal to 0 25b - 5500 = 0 To solve for b, we [URL=' this equation into our search engine[/URL] and we get: [B]b = 220[/B]

The square of a number is always nonnegative. This is true, and here is why: Suppose you have a positive number n. n^2 = n * n A positive times a positive is a positive Suppose you have a negative number -n (-n)^2 = -n * -n = n^2 A negative times a negative is a positive.

The square of a number is positive N ca be positive or negative, so test both scenarios: Take a positive number n. n^2 = n^2 * n^2 or Positive * Positive which is positive Take a negative number n (-n)^2 = -n * -n or Negative * Negative which is positive (-n)^2 = n^2

The square of a positive integer minus twice its consecutive integer is equal to 22. Find the integers. Let x = the original positive integer. We have: [LIST] [*]Consecutive integer is x + 1 [*]x^2 - 2(x + 1) = 22 [/LIST] Multiply through: x^2 - 2x - 2 = 22 Subtract 22 from each side: x^2 - 2x - 24 = 0 Using our [URL=' calculator[/URL], we get: x = 6 and x = -4 Since the problem states [U]positive integers[/U], we use: x = 6 and x + 1 = 7 [B](6, 7)[/B]

The square of the difference of a number and 4 A number means an arbitrary variable, let's call it x The difference of a number and 4: x - 4 The square of this difference: [B](x - 4)^2[/B]

The square of the difference of n and 2, increased by twice n The difference of n and 2: n - 2 The square of the difference of n and 2 means we raise (n - 2) to the 2nd power: (n - 2)^2 Twice n means we multiply n by 2: 2n The square of the difference of n and 2, increased by twice n [B](n - 2)^2 + 2n[/B]

the square of the sum of 2a and 3b the sum of 2a and 3b 2a + 3b The square of this sum means we raise 2a + 3b to the 2nd power: [B](2a + 3b)^2[/B]

the square of the sum of p and 5 The sum of p and 5 p + 5 Square this sum: [B](p + 5)^2[/B]

The square of the sum of twice a number x and y Take this in algebraic expression in 3 parts: [LIST=1] [*]Twice a number x means we multiply x by 2: 2x [*]The sum of twice a number x and y means we add y to 2x above: 2x + y [*]The square of the sum means we raise the sum (2x + y) to the second power below: [/LIST] [B](2x + y)^2[/B]

the square of the sum of two numbers Let the first number be x. Let the second number be y. The sum is: x + y Now we square that sum by raising the sum to a power of 2: [B](x + y)^2[/B]

the square of the sum of x and y is less than 20 The sum of x and y means we add y to x: x + y the square of the sum of x and y means we raise the term x + y to the 2nd power: (x + y)^2 The phrase [I]is less than[/I] means an inequality, so we write this as follows: [B](x + y)^2 < 20[/B]

Write this out, let the number be x. sqrt(2x) = x - 4 since 4 less means subtract Square each side: sqrt(2x)^2 = (x - 4)^2 2x = x^2 - 8x + 16 Subtract 2x from both sides x^2 - 10x + 16 = 0 Using the [URL=' calculator[/URL], we get two potential solutions x = (2, 8) Well, 2 does not work, since sqrt(2*2) = 2 which is not 4 less than 2 However, 8 does work: sqrt(2*8) = sqrt(16) = 4, which is 4 less than the number 8.

The store is selling apples for $0.49 per pound. Write a function to model the cost of "p" pounds of apples. Let p be the pounds of apples. Our cost function is: [B]C(p) = 0.49p[/B]

The sum of -4x^2 - 5x + 7 and 2x^2 + 8x - 11 can be written in the form ax^2 + bx + c, where a, b, and c are constants. What is the value of a + b + c? The sum means we add the polynomials together. We do this by adding the like terms: -4x^2 - 5x + 7 + 2x^2 + 8x - 11 (-4 +2)x^2 + (-5 + 8)x +(7 - 11) -2x^2 + 3x - 4 We have (a, b, c) = (-2, 3, -4) The question asks for a + b + c a + b + c = -2 + 3 - 4 a + b + c = [B]-3[/B]

The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers? Let the first number be x. And the second number be y. We're given: [LIST=1] [*]y = x + 1 [*]x + y = 3x - 3 (less 3 means subtract 3) [/LIST] Substitute (1) into (2): x + x + 1 = 3x - 3 Combine like terms: 2x + 1 = 3x - 3 [URL=' this equation into the search engine[/URL], we get: x = 4 Substituting x = 4 into equation 1: y = 4 + 1 y = 5 So (x, y) = [B](4, 5)[/B]

The sum of 2 numbers is 18. 3 times the greater number exceeds 4 times the smaller number by 5. Find the numbers. Let the first number be x. The second number is y. We have: [LIST=1] [*]x + y = 18 [*]3x = 4y + 5 [/LIST] Rearrange (2), by subtracting 4y from each side: 3x - 4y = 5 So we have a system of equations: [LIST=1] [*]x + y = 18 [*]3x - 4y = 5 [/LIST] Using our [URL=' equations calculator[/URL], we get: [B]x = 11 y = 7[/B]

the sum of 2 numbers is 5. 5 times the larger number plus 4 times the smaller number is 37. Find the numbers Let the first small number be x. Let the second larger number be y. We're given: [LIST=1] [*]x + y = 5 [*]5y + 4x = 37 [/LIST] We can solve this 3 ways, using the following methods: [LIST=1] [*][URL=' Method[/URL] [*][URL=' Method[/URL] [*][URL=' Rule[/URL] [/LIST] No matter what method we choose, we get: [B]x = -12 y = 17 [/B] Let's check our work using equation 1: -12 + 17 ? 5 5 = 5 <-- Check Let's check our work using equation 2: 5(17) + 4(-12) ? 37 85 - 48 ? 37 37 = 37 <-- Check

The sum of 2 numbers is 60. The larger number is thrice the smaller. Let the 2 numbers be x and y, where x is the smaller number and y is the larger number. We are given: [LIST=1] [*]x + y = 60 [*]y = 3x [/LIST] Substitute (2) into (1): x + (3x) = 60 Combine like terms: 4x = 60 [URL=' 4x = 60 into our search engine[/URL], and you get [B]x = 15[/B]. Substituting x = 15 into Equation (2) above, we get: y = 3(15) [B]y = 45 [/B] Check our work in Equation (1): 15 + 45 ? 60 60 = 60 Check our work in Equation (2): 45 ? 15(3) 45 = 45 The numbers check out, so our answer is [B](x, y) = (15, 45)[/B]

The sum of 2 numbers is 70. The difference of these numbers is 24. Write and solve a system of equations to determine the numbers. Let the two numbers be x and y. We have the following equations: [LIST=1] [*]x + y = 70 [*]x - y = 24 [/LIST] Add (1) to (2): 2x = 94 Divide each side by 2 [B]x = 47[/B] Plug this into (1) 47 + y = 70 Subtract 47 from each side, we have: [B]y = 23[/B]

the sum of 2 times a number and -2, added to 4 times a number. The phrase, [I]a number[/I], means an arbitrary variable, let's call it x. 2 times a number 2x The sum of means add, so we add -2, which is the same as subtracting 2 2x - 2 Now, we add 4 times x 2x - 2 + 4x Combining like terms, we have: (2 + 4)x - 2 [B]6x - 2[/B]

the sum of 23 and victor age is 59 Let's Victor's age be a. The sum of 23 and Victor's age (a) mean we add a to 23: 23 + a The word [I]is[/I] means an equation, so we set 23 + a equal to 59: [B]23 + a = 59[/B] <-- This is our algebraic expression Now if the problem asks you to take it a step further and solve this for a, [URL=' type this equation into our search engine[/URL] and we get: [B]a = 36[/B]

The sum of 3 consecutive integers is greater than 30. Let the first consecutive integer be n The second consecutive integer is n + 1 The third consecutive integer is n + 2 The sum is written as: n + n + 1 + n + 2 Combine like terms: (n + n + n) + (1 + 2) 3n + 3 The phrase [I]greater than[/I] means an inequality, which we write as: [B]3n + 3 > 30[/B]

the sum of 3 consecutive natural numbers, the first of which is n Natural numbers are counting numbers, so we the following expression: n + (n + 1) + (n + 2) Combine n terms and constants: (n + n + n) + (1 + 2) [B]3n + 3 Also expressed as 3(n + 1)[/B]

the sum of 3 consecutive natural numbers, the first of which is n We have: n + (n + 1) + (n + 2) Grouping like terms, we have: [B]3n + 3[/B]

The sum of 3 consecutive natural numbers, the first of which is n. We have 3 numbers: n, n + 1, and n + 2 Add them up: n + (n + 1) + (n + 2) Group like terms: [B]3n + 3[/B]

the sum of 3 numbers divided by its product The phrase [I]3 numbers[/I] means we choose [I]3[/I] arbitrary variables. Let's call them x, y, z. The sum of of these 3 numbers is: x + y + z The phrase [I]its product[/I] means we multiply all 3 arbitrary variables together: xyz Now, the phrase [I]divided by[/I] means we divide x + y + z by xyz: [B](x + y + z)/xyz[/B]

The sum of 3h and k divided by 2 The sum of 3h and k 3h + k Divided by 2: [B](3h + k)/2[/B]

The sum of 3w and 5 cubed The sum of 3w and 5: 3w + 5 The word [I]cubed[/I] means we raise 3w + 5 to the power 3: [B](3w + 5)^3[/B]

The sum of 4 and x is multiplied by 5. The result is then taken away from 16. Take this algebraic expression in 3 parts: [U]Part 1: The sum of 4 and x:[/U] 4 + x [U]Part 2: Multiplied by 5:[/U] 5(4 + x) [U]Part 3: The result is then taken away from 16:[/U] [B]16 - 5(4 + x)[/B]

the sum of 4 and x split into 5 equal parts The sum of x and 4 means we add 4 to x: x + 4 Whenever you see the phrase [I]split into[/I], think of divide or divided by: [B](x + 4)/5[/B]

The sum of 5 odd consecutive numbers is 145. Let the first odd number be n. We have the other 4 odd numbers denoted as: [LIST] [*]n + 2 [*]n + 4 [*]n + 6 [*]n + 8 [/LIST] Add them all together n + (n + 2) + (n + 4) + (n + 6) + (n + 8) The sum of the 5 odd consecutive numbers equals 145 n + (n + 2) + (n + 4) + (n + 6) + (n + 8) = 145 Combine like terms: 5n + 20 = 145 Using our [URL=' solver[/URL], we get [B]n = 25[/B]. Using our other 4 consecutive odd numbers above, we get: [LIST] [*]27 [*]29 [*]31 [*]33 [/LIST] Adding the sum up, we get: 25 + 27 + 29 + 31 + 33 = 145. So our 5 odd consecutive number added to get 145 are [B]{25, 27, 29, 31, 33}[/B]. [MEDIA=youtube]0T2PDuQIIwI[/MEDIA]

The sum of 80 and 40 is divided by 5 The sum of 80 and 40: 80 + 40 Divided by 5: [B](80 + 40)/5[/B]

The sum of a and b divided by their product The sum of a and b means we add b to a: a + b The product of a and b means we multiply a by b: ab To get our final algebraic expression, we divide the sum (a + b) by the product ab: [B](a + b)/ab[/B]

the sum of a and b, divided by the product of c and d The sum of a and b, means we add b to a a + b The product of c and d means we multiply c by d cd Divided by means we divide a + b by cd [B](a + b)/cd[/B]

The sum of a number and 5 all divided by 2 is 17 The phrase [I]a number[/I] means an arbitrary variable, let's call it x x The sum of a number and 5: x + 5 All divided by 2: (x + 5)/2 The word [I]is[/I] means equal to, so we set (x + 5)/2 equal to 17: [B](x + 5)/2 = 17[/B]

The sum of a number and 5 divided by 8. Let's take this algebraic expression in parts. Part 1: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Part 2: The sum of a number and 5 means we add 5 to the number x x + 5 Part 3: Next, we divide this expression by 8 [B](x + 5)/8[/B]

The sum of d and v, all multiplied by 8 This is an algebraic expression. The sum of d and v: d + v Multiply this sum by 8: [B]8(d + v)[/B]

The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age. How old are they now? Let Jocelyn's age be a Let Joseph's age be b. We're given two equations: [LIST=1] [*]a + b = 40 [*]2(a + 5) = b + 5 [/LIST] We rearrange equation (1) in terms of a to get: [LIST=1] [*]a = 40 - b [*]2a = b + 5 [/LIST] Substitute equation (1) into equation (2) for a: 2(40 - b) = b + 5 80 - 2b = b + 5 To solve this equation for b, we [URL=' it in our search engine[/URL] and we get: [B]b (Joseph's age) = 25[/B] Now, substitute b = 25 into equation (1) to solve for a: a = 40 - 25 [B]a (Jocelyn's age) = 15[/B]

The sum of Juans age and Saras age is 33 yrs. If Sara is 15 yrs old, how old is Juan? Let j be Juan's age and s be Sara's age. We have the following equations: [LIST=1] [*]j + s = 33 [*]s = 15 [/LIST] Substitute (2) into (1) j + 15 = 33 Using our [URL=' solver[/URL], we get[B] j = 18[/B]

The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages? [U]Givens[/U] [LIST] [*]Let Mr. Adam's age be a [*]Let Mrs. Benson's age be b [*]We're given two equations where [I]sum[/I] means we add and [I]difference[/I] means we subtract: [/LIST] [LIST=1] [*]a + b = 55 [*]a - b = 3 [/LIST] Since we have opposite coefficients for b, we can take a shortcut and add equation 1 to equation 2: (a + a) + (b - b) = 55 + 3 Combining like terms and simplifying, we get: 2a = 58 To solve this equation for a, we [URL=' it in our search engine[/URL] and we get: a = [B]29 [/B] If a = 29, then we plug this into equation (1) to get: 29 + b = 55 b = 55 - 29 b = [B]26 [MEDIA=youtube]WwkpNqPvHs8[/MEDIA][/B]

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now? Let Levi's current age be l. Let Renee's current age be r. Were given two equations: [LIST=1] [*]l + r = 89 [*]l - 7 = 4(r - 7) [/LIST] Simplify equation 2 by multiplying through: [LIST=1] [*]l + r = 89 [*]l - 7 = 4r - 28 [/LIST] Rearrange equation 1 to solve for r and isolate l by subtracting l from each side: [LIST=1] [*]r = 89 - l [*]l - 7 = 4r - 28 [/LIST] Now substitute equation (1) into equation (2): l - 7 = 4(89 - l) - 28 l - 7 = 356 - 4l - 28 l - 7 = 328 - 4l To solve for l, we [URL=' the equation into our search engine[/URL] and we get: l = [B]67[/B]

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times the unit digit. Find the number. Let the digits be (x)(y) where t is the tens digit, and o is the ones digit. We're given: [LIST=1] [*]x + y = 10 [*]10x+ y = 15y + 4 [/LIST] Simplifying Equation (2) by subtracting y from each side, we get: 10x = 14y + 4 Rearranging equation (1), we get: x = 10 - y Substitute this into simplified equation (2): 10(10 - y) = 14y + 4 100 - 10y = 14y + 4 [URL=' this equation into our search engine[/URL], we get: y = 4 Plug this into rearranged equation (1), we get: x = 10 - 4 x = 6 So our number xy is [B]64[/B]. Let's check our work against equation (1): 6 + 4 ? 10 10 = 10 Let's check our work against equation (2): 10(6)+ 4 ? 15(4) + 4 60 + 4 ? 60 + 4 64 = 64

The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number by 18. What is the number? Let x and (16-x) represent the original ten and units digits respectively Reversing its digits increases the number by 18 Set up the relational equation [10x + (16-x)] + 18 = 10(16 - x) + x Solving for x 9x + 34 = 160 - 9x Combine like terms 18x = 126 Divide each side of the equation by 18 18x/18 = 126/18 x = 7 So 16 - x = 16 - 7 = 9 The first number is 79, the other number is 97. and 97 - 79 = 18 so we match up. The number in our answer is [B]79[/B]

The sum of the squares of two consecutive positive integers is 61. Find these two numbers. Let the 2 consecutive integers be x and x + 1. We have: x^2 + (x + 1)^2 = 61 Simplify: x^2 + x^2 + 2x + 1 = 61 2x^2 + 2x + 1 = 61 Subtract 61 from each side: 2x^2 + 2x - 60 = 0 Divide each side by 2 x^2 + x - 30 Using our [URL=' equation calculator[/URL], we get: x = 5 and x = -6 The question asks for [I]positive integers[/I], so we use [B]x = 5. [/B]This means the other number is [B]6[/B].

The sum of the sum of x and z and the difference of y and z Take this algebraic expression in 3 parts: Step 1: The sum of x and z is written as: x + z Step 2: The difference of y and z is written as: y - z Step 3: the sum of the sum and difference is written as: x + z + (y - z) x + z + y - z Cancelling the z terms, we get: [B]x + y [MEDIA=youtube]bmoZXImYCrg[/MEDIA][/B]

Let the 3 integers be x, y, and z. y = x + 1 z = y + 1, or x + 2. Set up our equation: x + (x + 1) + (x + 2) = 42 Group our variables and constants: (x + x + x) + (1 + 2) = 42 3x + 3 = 42 Subtract 3 from each side: 3x = 39 Divide each side of the equation by 3: [B]x = 13 So y = x + 1 = 14 z = x + 2 = 15 (x,y,z) = (13,14,15)[/B]

The sum of three numbers is 171. The second number is 1/2 of the first and the third is 3/4 of the first. Find the numbers. We have three numbers, x, y, and z. [LIST=1] [*]x + y + z = 171 [*]y = 1/2x [*]z = 3/4x [/LIST] Substitute (2) and (3) into (1) x + 1/2x + 3/4x = 171 Use a common denominator of 4 for each x term 4x/4 + 2x/4 + 3x/4 = 171 (4 + 2 + 3)x/4 = 171 9x/4 = 171 [URL=' this equation into our search engine[/URL], and we get [B]x = 76[/B] So y = 1/2(76) --> [B]y = 38[/B] Then z = 3/4(76) --> [B]z = 57[/B]

The sum of twice an integer and 3 times the next consecutive integer is 48 Let the first integer be n This means the next consecutive integer is n + 1 Twice an integer means we multiply n by 2: 2n 3 times the next consecutive integer means we multiply (n + 1) by 3 3(n + 1) The sum of these is: 2n + 3(n + 1) The word [I]is[/I] means equal to, so we set 2n + 3(n + 1) equal to 48: 2n + 3(n + 1) = 48 Solve for [I]n[/I] in the equation 2n + 3(n + 1) = 48 We first need to simplify the expression removing parentheses Simplify 3(n + 1): Distribute the 3 to each term in (n+1) 3 * n = (3 * 1)n = 3n 3 * 1 = (3 * 1) = 3 Our Total expanded term is 3n + 3 Our updated term to work with is 2n + 3n + 3 = 48 We first need to simplify the expression removing parentheses Our updated term to work with is 2n + 3n + 3 = 48 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (2 + 3)n = 5n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 5n + 3 = + 48 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 3 and 48. To do that, we subtract 3 from both sides 5n + 3 - 3 = 48 - 3 [SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE] 5n = 45 [SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE] 5n/5 = 45/5 Cancel the 5's on the left side and we get: n = [B]9[/B]

The sum of two consecutive integers if n is the first integer. consecutive means immediately after, so we have: n n + 1 [U]The sum is written as:[/U] n + n + 1 [U]Grouping like terms, we have:[/U] (n + n) + 1 [B]2n + 1[/B]

The sum of two consecutive integers plus 18 is 123. Let our first integer be n and our next integer be n + 1. We have: n + (n + 1) + 18 = 123 Group like terms to get our algebraic expression: 2n + 19 = 123 If we want to solve the algebraic expression using our [URL=' solver[/URL], we get n = 52. This means the next integer is 52 + 1 = 53

Let x be the larger number. Let y be the smaller number. We're given two equations: [LIST=1] [*]x + y = 231 [*]x = 2y [/LIST] Substitute (2) into (1) for x: 2y + y = 231 3y = 231 [URL=' this into our math solver[/URL] and get y = 77 This means x is: x = 2(77) x = [B]154[/B]

Choose two variables as arbitrary numbers, let's say x and y [U]The sum of x and y is:[/U] x + y [U]Multiply that by 9[/U] [B]9(x + y)[/B]

The sum of two y and the quantity of three plus y plus twice the quantity two y minus two equals fifteen The sum of two y and the quantity of three plus y 2y + (3 + y) twice the quantity two y minus two 2(2y - 2) The sum of two y and the quantity of three plus y plus twice the quantity two y minus two 2y + (3 + y) + 2(2y - 2) Equals 15 to get our algebraic expression [B]2y + (3 + y) + 2(2y - 2) = 15[/B] [B][/B] If the problem asks you to solve for yL 2y + 3 + y + 4y - 4 = 15 Group like terms: 7y - 1 = 15 Add 1 each side: 7y = 16 Divide each side by 7: y = [B]16/7[/B]

the sum of w and v divided by their difference the sum of w and v: w + v their difference: w - v the sum of w and v divided by their difference [B](w + v)/(w - v)[/B]

The sum of x and 10 equals the sum of 2 times x and 12 The sum of x and 10 means we add 10 to x: x + 10 2 times x means we multiply x by 2: 2x the sum of 2 times x and 12 means we add 12 to 2x: 2x + 12 The sum of x and 10 equals the sum of 2 times x and 12: x + 10 + (2x + 12) Distribute the parentheses, and we get: x + 10 + 2x + 12 Group like terms: (1 + 2)x + 10 + 12 [B]3x + 22[/B]

the sum of x and 3 is divided by 2 The sum of x and 3 x + 3 Divide this expression by 2 (x + 3)/2

the sum of X and 3 is divided by 2 The sum of X and 3 X + 3 Is divided by 2 [B](X + 3)/2[/B]

The sum of x and one half of x To write this algebraic expression correctly, we have (1 + 1/2)x To get common denominators, we write 1 as 2/2. So we have: (2/2 + 1/2)x [B]3/2x[/B]

The sum of x and y doubled The sum of x and y: x + y Double it [B]2(x + y)[/B]

The sum of x and y is multiplied by 6. [LIST] [*]The sum of x and y: x + y [*]Multiply the sum by 6: [/LIST] [B]6(x + y)[/B]

The sum of y and z decreased by the difference of m and n. Take this algebraic expression in 3 parts: [LIST=1] [*]The sum of y and z means we add z to y: y + z [*]The difference of m and n means we subtract n from m: m - n [*]The phrase [I]decreased by[/I] means we subtract the quantity (m - n) from the sum (y + z) [/LIST] [B](y + z) - (m - n)[/B]

The tax on 1 dollar is 7 cents. What is the tax on 5 dollars? Two ways you can do this: [LIST=1] [*]Every 1 dollar has 7 cents, so every 5 dollars has (1 * 5) = (7 * 5) = [B]35 cents[/B] [*]7 cents is 7% of 1 dollar. So 7% of 5 dollars is [B]35 cents[/B] [/LIST]

The teacher is handing out note cards to her students. She gave 20 note cards to the first student, 30 note cards to the second student, 40 note cards to the third student, and 50 note cards to the fourth student. If this pattern continues, how many note cards will the teacher give to the fifth student? [LIST] [*]Student 1 has 20 [*]Student 2 has 30 [*]Student 3 has 40 [*]Student 4 has 50 [/LIST] The teacher adds 10 note cards to each student. Or, if we want to put in a sequence formula, we have: S(n) = 10 + 10n where n is the student number Simplified, we write this as: S(n) = 10(1 + n) The question asks for S(5) S(5) = 10(1 + 5) S(5) = 10(6) [B]S(5) = 60 [/B] If we wanted to simply add 10 and not use a sequence formula, we see that S(4) = 50. So S(5) = S(4) + 10 S(5) = 50 + 10 [B]S(5) = 60[/B]

The team A scored 13 more points than Team B. The total of their score was 47. How many points did team A score? Let a be the amount of points A scored, and b be the amount of points B scored. We're given: [LIST=1] [*]a = b + 13 [*]a + b = 47 [/LIST] Plug (1) into (2) (b + 13) + b = 47 Combine like terms: 2b + 13 = 47 [URL=' this equation into our search engine[/URL], we get: b = 17 Now plug this into (1): a = 17 + 13 a = [B]30[/B]

The temperature in Chicago was five (5) degrees Celsius in the morning and is expected to drop by as much as 12 degrees during the day. What is the lowest temperature in Chicago for the day? We start with 5 celsius A drop in temperature means we subtract 5 - 12 = [B]-7 or 7 degrees below zero[/B]

The temperature inside the lab refrigerator is no more than 35 . Use t to represent the temperature (in ) of the refrigerator. The phrase [I]no more than[/I] means less than or equal to. We have this inequality: [B]t <= 35[/B]

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins? Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given: [LIST=1] [*]a + h + c = 48 [*]a = 0.5h [*]a = c + 4 [/LIST] To isolate equations in terms of Suresh's age (a), let's do the following: [LIST] [*]Rewriting (3) by subtracting 4 from each side, we get c = a - 4 [*]Rewriting (2) by multiply each side by 2, we have h = 2a [/LIST] We have a new system of equations: [LIST=1] [*]a + h + c = 48 [*]h = 2a [*]c = a - 4 [/LIST] Plug (2) and (3) into (1) a + (2a) + (a - 4) = 48 Group like terms: (1 + 2 + 1)a - 4 = 48 4a - 4 = 48 [URL=' this equation into our search engine[/URL], we get: [B]a = 13 [/B]<-- Suresh's age This means that Hakima's age, from modified equation (2) above is: h = 2(13) [B]h = 26[/B] <-- Hakima's age This means that Saad's age, from modified equation (3) above is: c = 13 - 4 [B]c = 9[/B] <-- Saad's age [B] [/B]

The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equation that models the cost of each bracelet. We set up a cost function as fixed cost plus total cost. Fixed cost is the shipping charge of $9. So we have the following cost function where n is the cost of the bracelets: C(b) = nb + 9 We are given C(9) = 72 and b = 9 9n + 9 = 72 [URL=' this through our equation calculator[/URL], and we get [B]n = 7[/B].

The total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25 [U]Set up the cost function:[/U] Cost function = Fixed Cost + Variable Cost per Unit * Number of Units [U]Plug in Fixed Cost = 2900 and Cost per Unit = $25[/U] [B]C(x) = 2900 + 25x [MEDIA=youtube]77PiD-VADjM[/MEDIA][/B]

the total of a and 352 equals a divided by 195 Take this algebraic expression in 3 parts: [LIST=1] [*]The total of a and 352 means we add 352 to a: a + 352 [*]a divided by 195: a/195 [*]The phrase [I]equals[/I] means we set (1) equal to (2) to get our final algebraic expression: [/LIST] [B]a + 352 = a/195[/B]

The total of z and 12 multiplied by the difference of 9 and y The total of z and 12: z + 12 The difference of 9 and y: 9 - y Now we multiply z + 12 by 9 - y: [B](z + 12)(9 - y)[/B]

the university of california tuition in 1990 was $951 and tuition has been increasing by a rate of 26% each year, what is the exponential formula Let y be the number of years since 1990. We have the formula T(y): [B]T(y) = 951 * 1.26^y[/B]

The value of 3 times the quantity of 4 + x is greater than 6 less than x. 3 times the quantity 4 + x 3(4 + x) 6 less than x x - 6 3 times the quantity 4 + x is greater than x - 6 [B]3(4 + x) > x - 6[/B]

The value of a company van is $15,000 and decreased at a rate of 4% each year. Approximate how much the van will be worth in 7 years. Each year, the van is worth 100% - 4% = 96%, or 0.96. We have the Book value equation: B(t) = 15000(0.96)^t where t is the time in years from now. The problem asks for B(7): B(7) = 15000(0.96)^7 B(7) = 15000(0.7514474781) B(7) = [B]11,271.71[/B]

The value of a stock begins at $0.07 and increases by $0.02 each month. Enter an equation representing the value of the stock v in any month m. Set up our equation v(m): [B]v(m) = 0.07 + 0.02m[/B]

The value of all the quarters and dimes in a parking meter is $18. There are twice as many quarters as dimes. What is the total number of dimes in the parking meter? Let q be the number of quarters. Let d be the number of dimes. We're given: [LIST=1] [*]q = 2d [*]0.10d + 0.25q = 18 [/LIST] Substitute (1) into (2): 0.10d + 0.25(2d) = 18 0.10d + 0.5d = 18 [URL=' this equation into our search engine[/URL], and we get [B]d = 30[/B].

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take? Set up the earnings equation for the volleyball team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 4w + 81 Set up the earnings equation for the wrestling team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 2w + 85 If the raised the same amount in total, set both earnings equations equal to each other: 4w + 81 = 2w + 85 Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides 4w + 81 - 2w = 2w + 85 - 2w [SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE] 2w + 81 = 85 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 81 and 85. To do that, we subtract 81 from both sides 2w + 81 - 81 = 85 - 81 [SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE] 2w = 4 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2w/2 = 4/2 w = [B]2 <-- How many cars it will take [/B] To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2: E = 4(2) + 81 E = 8 + 81 E = [B]89 <-- Total Earnings[/B]

The Waist to Hip Ratio (WHR) is commonly expressed as a decimal. WHR has been shown to be a good predictor of possible cardiovascular problems in both men and women. If Jonia has a WHR greater than 1, she is at high risk for cardiovascular problems. Jonias waist measurement is 42 inches and her hip measurement 2 inches less. Jonia's WHR: WHR = W/H WHR = 42/(42 - 2) WHR =4 2/40 WHR = [B]1.5 which is high risk[/B]

The weight of water is approximately 2 pounds 3 ounces per litre. How much will 8 litres of water weigh? First, convert 2 pounds 3 ounces to ounces. 16 ounces to a pound, so we have: 2(16) + 3 32 + 3 35 ounces for one liter For 8 litres, we have: 35 * 8 = 280 ounces Now, convert that back to pounds 280/16 = [B]17.5 pounds, or 17 pounds, 8 ounces.[/B]

The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2 The Area (A) of a rectangle is given by: A = lw With an area of [I]less than[/I] 86 and a width of 4, we have the following inequality: 4l < 86 To solve for l, we [URL=' this inequality into our search engine[/URL] and we get: [B]l < 21.5[/B]

The of 5 and 7 is 12 [B](sum) or (total) since 5 + 7 = 12[/B]

there are $4.20 in nickel and quarters. There are 6 more nickels than quarters there. How many coins of each are there We're given two equations: [LIST=1] [*]n = q + 6 [*]0.05n + 0.25q = 4.2 [/LIST] Substitute equation (1) into equation (2): 0.05(q + 6) + 0.25q = 4.2 Multiply through and simplify: 0.05q + 0.3 + 0.25q 0.3q + 0.3 = 4.2 To solve for q, we [URL=' this equation into the search engine[/URL] and we get: q = [B]13 [/B] To solve for n, we plug in q = 13 into equation (1): n = 13 + 6 n = [B]19[/B]

There are 10 more cars(c) than jeeps(j) [B]c = j + 10[/B]

There are 100 people in a sport centre. 67 people use the gym. 62 people use the swimming pool. 56 people use the track. 38 people use the gym and the pool. 31 people use the pool and the track. 33 people use the gym and the track. 16 people use all three facilities. A person is selected at random. What is the probability that this person doesn't use any facility? WE use the compound probability formula for 3 events: [LIST=1] [*]Gym use (G) [*]Swimming pool use (S) [*]Track (T) [/LIST] P(G U S U T) = P(G) + P(S) + P(T) - P(G Intersection S) - P(G Intersection T) - P(S Intersection T) + P(G Intersection S Intersection T) [LIST] [*]Note: U means Union (Or) and Intersection means (And) [/LIST] Plugging our numbers in: P(G U S U T) = 67/100 + 62/100 + 56/100 - 38/100 - 31/100 - 33/100 + 16/100 P(G U S U T) = (67 + 62 + 56 - 38 - 31 - 33 + 16)/100 P(G U S U T) = 99/100 or 0.99 What this says is, the probability that somebody uses at any of the 3 facilities is 99/100. The problem asks for none of the 3 facilities, or P(G U S U T)' P(G U S U T)' = 1 - P(G U S U T) P(G U S U T)' = 1 - 99/100 P(G U S U T)' = 100/100 - 99/100 P(G U S U T)' = [B]1/100 or 0.1[/B]

There are 1000 juniors in a college. Among the 1000 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses. a) What is the probability that a randomly selected junior is taking at least one of these two courses? b) What is the probability that a randomly selected junior is taking PSYC300, given that he/she is taking STAT200? a) P(A U B) = P(A) + P(B) - P(A ? B) = 0.2 + 0.1 - 0.05 = [B]0.25[/B] b) P(SYC|STAT) = P(STAT ? SYC)/P(STAT) = 0.05/0.2 = [B]0.25[/B]

There are 113 identical plastic chips numbered 1 through 113 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is greater than 44? We want 45, 46, 113 The formula to get inclusive number count between and including 2 numbers is: Total numbers = L - S + 1 Total numbers = 113 - 45 + 1 Total numbers = 69 That is 69 possible numbers. We draw this out of a total of 113 [B]P(Number > 44) = 69/113 [B]P(Number > 44) [/B]= 0.610619 [MEDIA=youtube]BLBVcpdHqXU[/MEDIA][/B]

There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How many of each animal are there? Chickens have 2 legs, pigs have 4 legs. Let c be the number of chickens and p be the number of pigs. Set up our givens: (1) c + p = 13 (2) 2c + 4p = 40 [U]Rearrange (1) to solve for c by subtracting p from both sides:[/U] (3) c = 13 - p [U]Substitute (3) into (2)[/U] 2(13 - p) + 4p = 40 26 - 2p + 4p = 40 [U]Combine p terms[/U] 2p + 26 = 40 [U]Subtract 26 from each side:[/U] 2p = 14 [U]Divide each side by 2[/U] [B]p = 7[/B] [U]Substitute p = 7 into (3)[/U] c = 13 - 7 [B]c = 6[/B] For a shortcut, you could use our [URL=' equations calculator[/URL]

There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults? We set up an equation to represent this: 5x + 3x = 144 [URL=' this equation into our search engine[/URL], we get: x = 18 This means we have: Adults = 5(18) [B]Adults = 90[/B] Children = 3(18) [B]Children = 54[/B]

[SIZE=6]There are 144 people in the audience. The ratio of adults to children is 5 to 3. How many adults are there? Let x be the number of people, we have: 5x + 3x = 144 [/SIZE] [URL=' this problem in our search[/SIZE][/URL][SIZE=6][URL=' engine[/URL], we get x = 18. Which means we have 5(18) = [B]90 adults[/B][/SIZE]

There are 15 cards, numbered 1 through 15. If you pick a card, what is the probability that you choose an odd number or a two? We want the P(odd) or P(2). P(odd) = 1, 3, 5, 7, 9, 11, 13, 15 = 8/15 P(2) = 1/15 Add them both: 8/15 + 1/15 = 9/15 Simplified, we get [B]3/5[/B].

There are 2 consecutive integers. Twice the first increased by the second yields 16. What are the numbers? Let x be the first integer. y = x + 1 is the next integer. We have the following givens: [LIST=1] [*]2x + y = 16 [*]y = x + 1 [/LIST] Substitute (2) into (1) 2x + (x + 1) = 16 Combine x terms 3x + 1 = 16 Subtract 1 from each side 3x = 15 Divide each side by 3 [B]x = 5[/B] So the other integer is 5 + 1 = [B]6[/B]

There are 250 boys and 150 girls in a school, if 60% of the boys and 40% of the girls play football, what percentage of the school play football [U]First calculate total students:[/U] Total students = Boys + Girls Total students = 250 + 150 Total students = 400 [U]Calculate the boys that play football:[/U] Boys playing football = 60% * 250 [URL=' playing football [/URL]= 150 [U]Calculate the girls that play football:[/U] Girls playing football = 40% * 150 [URL=' playing football[/URL][URL=' [/URL]= 60 [U]Calculate total people playing football[/U]: Total people playing football = Boys playing football + Girls playing football Total people playing football = 150 + 60 Total people playing football = 210 Calculate percentage of the school playing football (P): P = 100% * Total people playing football / Total Students P = 100% * [URL=' P = 100% * 0.525 P = [B]52.5%[/B]

There are 30 students in a classroom. Eighteen students read [I]A Wrinkle in Time[/I] while 22 children read [I]The Hobbit[/I]. If all children read at least one of the books, how many read both books? 30 - 18 = 12 students read the Hobbit only 30 - (12 + 8) = [B]10 students who read both[/B]

There are 32 female performers in a dance recital. The ratio of men to women is 3:8. How many men are in the dance recital? 3:8 = x:32 3/8 = x/32 Cross multiply: 8x = 96 Divide each side by 8 x = 12 Check our work: 12:32 Divide each part by 4 12/4 = 3 and 32/4 = 8 so we have 3:8 :)

Let b = boys and g = girls. We have two equations: (1) b + g = 320 (2) g = b + 24 Substitute (2) into (1) for g b + (b + 24) = 320 Combine b terms: 2b + 24 = 320 Use our [URL=' calculator[/URL]: [B]b = 148 [/B] Substitute b = 148 into (2) g = 148 + 24 [B]g = 172[/B]

There are 33 students in an Algebra I class. There are 7 fewer girls than boys. How many girls are in the class? Let b be the number of boys and g be the number of girls. We are given 2 equations: [LIST=1] [*]g = b - 7 [*]b + g = 33 [/LIST] Substitute (1) into (2): b + (b - 7) = 33 Combine like terms: 2b - 7 = 33 [URL=' this equation into our search engine[/URL], we get b = 20. Since the problem asks for how many girls (g) we have, we substitute b = 20 into Equation (1): g = 20 - 7 [B]g = 13[/B]

There are 5 orange books, 12 black books, and 8 tan books on Mr. Johnsons bookshelf. Calculate the probability of randomly selecting a black book and then a tan book without replacement. Write your answer as a percent. P(black book first draw) P(black book first draw) = 12 black / (5 orange + 12 black + 8 tan) P(black book first draw) = 12 / 25 P(tan book second draw) P(tan book second draw) = 8 tan / (5 orange + 11 black + 8 tan) <-- 11 black because we already drew one black P(tan book second draw) = 8 / 24 Using our fraction reduction calculator, this simplifies to 1/3 Since each draw is independent, we multiply both probabilities: P(black book first draw, tan book second draw) = 12/25 * 1/3 P(black book first draw, tan book second draw) = 12/75 P(black book first draw, tan book second draw) = [B]16%[/B]

[SIZE=4]There are 5 pencil-cases on the desk. Each pencil-case contains at least 10 pencils, but not more than 14 pencils. Which of the following could be the total number of pencils in all 5 cases? A) 35 B) 45 C) 65 D) 75 [U]Determine the minimum amount of pencils (At least means greater than or equal to):[/U] Minimum Amount of pencils = Cases * Min Quantity Minimum Amount of pencils = 5 * 10 Minimum Amount of pencils = 50 [SIZE=4][U]Determine the maximum amount of pencils (Not more than means less than or equal to):[/U] Maximum Amount of pencils = Cases * Min Quantity Maximum Amount of pencils = 5 * 14 Maximum Amount of pencils = 70[/SIZE] So our range of pencils (p) is: 50 <= p <= 70 Now take a look at our answer choices. The only answer which fits in this inequality range is [B]C, 65[/B]. [B][/B][/SIZE]

There are 5 red and 4 black balls in a box. If you pick out 2 balls without replacement, what is the probability of getiing at least one red ball? First list out our sample space. At least one means 1 or 2 red balls, so we have 3 possible draws: [LIST=1] [*]Red, Black [*]Black, Red [*]Red, Red [/LIST] List out the probabilities: [LIST=1] [*]Red (5/9) * Black (4/8) = 5/18 [*]Black (4/9) * Red (5/8) = 5/18 [*]Red (5/9) * Red (4/8) = 5/18 [/LIST] Add these up: 3(5)/18 = [B]5/6[/B]

There are 63 students in middle school chorus. There are 11 more boys than girls. How many boys x and girls y are in the chorus? Set up equations: [LIST=1] [*]x + y = 63 [*]x = y + 11 [/LIST] Substitute (1) into (2) y + 11 + y = 63 2y + 11 = 63 Use our [URL=' solver[/URL]: [B]y = 26[/B]

There are 64 members in the history club. 11 less than half of the members are girls. How many members are boys? Set up two equations where b = the number of boys and g = the number of girls [LIST=1] [*]b + g = 64 [*]1/2(b + g) - 11 = g [/LIST] Substitute (1) for b + g into (2) 1/2(64) - 11 = g 32 - 11 = g [B]g = 21[/B] Substitute g = 21 into (1) b + 21 = 64 Using our [URL=' calculator[/URL], we get: [B]b = 43[/B]

There are 72 boys and 90 girls on the Math team For the next math competition Mr Johnson would like to arrange all of the students in equal rows with only girls or boys in each row with only girls or boys in each row. What is the greatest number of students that can be put in each row? To find the maximum number (n) of boys or girls in each row, we want the GCF (Greatest Common Factor) of 72 and 90. [URL=' our GCF calculator for GCF(72,90)[/URL], we get 18. [LIST] [*]72 boys divided by 18 = [B]4 rows of boys[/B] [*]90 girls divided by 18 = [B]5 rows of girls[/B] [/LIST]

[SIZE=6]There are 812 students in a school. There are 36 more girls than boys. How many girls are there? Let b be boys Let g be girls We're given two equations:[/SIZE] [LIST=1] [*][SIZE=6]b + g = 812[/SIZE] [*][SIZE=6]g = b + 36[/SIZE] [/LIST] [SIZE=6]Rearrange equation 2 to subtract b from each side: [/SIZE] [LIST=1] [SIZE=6] [LIST][*]b + g = 812[/LIST] [LIST][*]-b + g = 36[/LIST][/SIZE] [/LIST] [SIZE=6]Add equation (1) to equation (2): b - b + 2g = 812 + 36 The b's cancel: 2g = 848 Divide each side by 2: 2g/2 = 848/2 g = [B]424[/B] [B][/B] To find b, we put g= 424 into equation 1: b + 424 = 812 b = 812 - 424 b = [B]388[/B] [MEDIA=youtube]JO1b7qVwWoI[/MEDIA] [/SIZE]

There are 9 buses, each of these buses is taking 35 people to a game. Another bus is taking 7 people. How many people are these buses taking to the game? We have 9 buses * 35 people each + another bus with 7 more people: 9(35) + 7 315 + 7 [B]322 people[/B]

There are cows and chickens in a barn along with a three-legged dog named Tripod. If there are twice as many chickens as cows, how many legs are there in the barn. (Call the number of cows n.) Number of cows = n Number of cows legs = 4n Number of chickens = 2n Number of chicken legs = 2*2n = 4n Tripod legs = 3 Total legs = 4n + 4n + 3 [B]8n + 3[/B]

There are only horses and ducks on a farm. There are 80 animals in all and the number of ducks is called n. How many horse legs are there on the farm? Number of duck legs = 2 legs * n ducks = 2n legs Number of horses = 80 - n Legs per horse = 4 Total horse legs = 4(80 - n) = [B]320 - 4n[/B]

There are thrice as many girls (g) as there are boys (b) Thrice means we multiply by 3, so we have the following algebraic expression: [B]g = 3b[/B]

There are two bells in the school. Bell A rings every 2 minutes. Bell B rings every 3 minutes. If both bells ring together at 8.02 p.m., when will they ring together again? Using our[URL=' least common multiple calculator,[/URL] we find the LCM(2, 3) = 6. Which means the next time both bells ring together is 6 minutes from now. 8:02 p.m. + 6 minutes = [B]8:08 p.m.[/B]

There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The difference between 2 times the first number and 3 times the second number is 24. Find the two numbers. Let the first number be x and the second number be y. We have 2 equations: [LIST=1] [*]4x + 3y = 24 [*]2x - 3y = 24 [/LIST] Without doing anything else, we can add the 2 equations together to eliminate the y term: (4x + 2x) + (3y - 3y) = (24 + 24) 6x = 48 Divide each side by 6: [B]x = 8 [/B] Substitute this into equation (1) 4(8) + 3y = 24 32 + 3y = 24 [URL=' 32 + 3y = 24 into our search engine[/URL] and we get [B]y = 2.6667[/B].

There is a bag filled with 3 blue, 4 red and 5 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting exactly 1 green? Calculate Total marbles Total marbles = Blue + Red + Green Total marbles = 3 + 4 + 5 Total marbles = 12 Probability of a green = 5/12 Probability of not green = 1 - 5/12 = 7/12 To get exactly one green in two draws, we either get a green, not green, or a not green, green [U]First Draw Green, Second Draw Not Green[/U] [LIST] [*]1st draw: Probability of a green = 5/12 [*]2nd draw: Probability of not green = 7/11 <-- 11 since we did not replace the first marble [*]To get the probability of the event, since each draw is independent, we multiply both probabilities [*]Probability of the event is (5/12) * (7/11) = 35/132 [/LIST] [U]First Draw Not Green, Second Draw Not Green[/U] [LIST] [*]1st draw: Probability of not a green = 7/12 [*]2nd draw: Probability of not green = 5/11 <-- 11 since we did not replace the first marble [*]To get the probability of the event, since each draw is independent, we multiply both probabilities [*]Probability of the event is (7/12) * (5/11) = 35/132 [/LIST] To get the probability of exactly one green, we add both of the events: First Draw Green, Second Draw Not Green + First Draw Not Green, Second Draw Not Green 35/132 + 35/132 = 70/132 [URL=' our fraction simplify calculator[/URL], we get: [B]35/66[/B]

There is a bag filled with 4 blue, 3 red and 5 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting 2 blues? We have (4 blue + 3 red + 5 green) = 12 total marbles With replacement, the probability of getting one blue is 4/12 = 1/3 Since each draw is independent of the last, the probability of Blue, Blue = 1/3 * 1/3 = [B]1/9[/B]

There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 blue? Find the total number of marbles in the bag: Total marbles = 5 blue + 6 red + 2 green Total marbles = 13 The problem asks for exactly one blue in 2 draws [I]with replacement[/I]. Which means you could draw as follows: Blue, Not Blue Not Blue, Blue The probability of drawing a blue is 5/13, since we replace the marbles in the bag each time. The probability of not drawing a blue is (6 + 2)/13 = 8/13 And since each of the 2 draws are independent of each other, we multiply the probability of each draw: Blue, Not Blue = 5/13 * 8/13 =40/169 Not Blue, Blue = 8/13 * 5/13 = 40/169 We add both probabilities since they both count under our scenario: 40/169 + 40/169 = 80/169 Checking our [URL=' simplification calculator[/URL], we see you cannot simplify this fraction anymore. So our probability stated in terms of a fraction is 80/169 [URL=' in terms of a decimal[/URL], it's 0.4734

There is a sales tax of $5 on an item that costs $51 before tax. A second item costs $173.40 before tax. What is the sales tax on the second item? Calculate the sales tax percent using the first item: Sales Tax Decimal = 100% * Sales Tax / Pre-Tax Bill Sales Tax Decimal = 100% * 5/51 Sales Tax Decimal = 0.098 Calculate the sales tax on the second item: Sales Tax = Pre-Tax bill * (1 + Sales Tax) Sales Tax = $173.40 (1 + 0.098) Sales Taax = $173.40 * 1.098 Sales Tax = [B]$190.39[/B]

There is a stack of 10 cards, each given a different number from 1 to 10. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an odd number and the second card is greater than 7. First Event: P(1, 3, 5, 7, 9) = 5/10 = 1/2 or 0.5 Second Event: P(8, 9, 10) = 3/10 or 0.3 Probability of both events since each is independent is 1/2 * 3/10 = 3/20 = [B]0.15 or 15%[/B]

There is an escalator that is 1090.3 feet long and drops a vertical distance of 193.4 feet. What is its angle of depression? The sin of the angle A is the length of the opposite side / hypotenuse. sin(A) = Opposite / Hypotenuse sin(A) = 193.4 / 1090/3 sin(A) = 0.1774 [URL=' want the arcsin(0.1774)[/URL]. [B]A = 10.1284[/B]

Set up two equations: (1) b = g + 16 (2) b + g = 150 Substitute equation (1) into (2) (g + 16) + g = 150 Combine like terms 2g + 16 = 150 Subtract 16 from each side 2g = 134 Divide each side by 2 to isolate g g = 67 Substitute this into equation (1) b = 67 + 16 [B]b = 83[/B]

There were 286,200 graphic designer jobs in a country in 2010. It has been projected that there will be 312,500 graphic designer jobs in 2020. (a) Using the data, find the number of graphic designer jobs as a linear function of the year. [B][U]Figure out the linear change from 2010 to 2020[/U][/B] Number of years = 2020 - 2010 Number of years = 10 [B][U]Figure out the number of graphic designer job increases:[/U][/B] Number of graphic designer job increases = 312,500 - 286,200 Number of graphic designer job increases = 26,300 [B][U]Figure out the number of graphic designer jobs added per year[/U][/B] Graphic designer jobs added per year = Total Number of Graphic Designer jobs added / Number of Years Graphic designer jobs added per year = 26,300 / 10 Graphic designer jobs added per year = 2,630 [U][B]Build the linear function for graphic designer jobs G(y) where y is the year:[/B][/U] G(y) = 286,200 + 2,630(y - 2010) [B][U]Multiply through and simplify:[/U][/B] G(y) = 286,200 + 2,630(y - 2010) G(y) = 286,200 + 2,630y - 5,286,300 [B]G(y) = 2,630y - 5,000,100[/B]

Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be 20. What is the number Let's call our number n. Double the number means we multiply n by 2: 2n Subtract 6 from the result means we subtract 6 from 2n: 2n - 6 Divide the answer by 2: (2n - 6)/2 We can simplify this as n - 3 The quotient will be 20. This means the simplified term above is set equal to 20: [B]n - 3 = 20 [/B] <-- This is our algebraic expression If you want to take it a step further, and solve for n in the algebraic expression above, we [URL=' this expression into our calculator[/URL], and get: n = 23

Thirty is half of the sum of 4 and a number. The phrase [I]a number[/I] represents an arbitrary variable, let's call it x. The sum of 4 and a number: 4 + x Half of this sum means we divide by 2: (4 + x)/2 Set this equal to 30: [B](4 + x)/2 = 30[/B] <-- This is our algebraic expression

Three ordinary dice are rolled. What is the probability that the results are all less than 5 Calculate individual die probabilities: [LIST] [*]Die 1 P(x < 5) = 4/6 = 2/3 [*]Die 2 P(x < 5) = 4/6 = 2/3 [*]Die 3 P(x < 5) = 4/6 = 2/3 [/LIST] Since each roll is independent, we have: P(Die 1 < 5, Die 2 < 5, Die 3 < 5) = 2/3 * 2/3 * 2/3 P(Die 1 < 5, Die 2 < 5, Die 3 < 5) = [B]8/27[/B]

Three people went to lunch and bought a large meal which they all split. The total cost, including tip, was $30. Each person paid $10 to the waitress and started to leave the restaurant. As they left, the waitress came running up to them with five dollars saying that she made a mistake and that the meal and tip should have cost only $25. The waitress then gave each person one dollar, but didn't know how to split the remaining two dollars. They told her to keep the extra two dollars as an additional tip. When the people started talking about what had just happened, they started getting confused. They had each paid $10 for the meal and received one dollar back, so they each really paid $9 for the meal for a total of $27. Add the two dollars of extra tip and the total is $29. Where did the extra one dollar go? [B]The missing dollar is not really missing. The cost of the meal is really $27. The $25 plus the extra two dollar tip was given to the waitress -- $27 What we have is the cost ($27) plus the refund ($3) = $30. The $30 that was originally paid is accounted for as follows: Restaurant + regular waitress tip: $25 Three people: $3 (refund) Waitress: $2 (extra tip) $25 + $3 + $2 = $30[/B]

Three tennis balls each have a radius of 2 inches. They are put into a 12 inch high cylinder with a 4 inch diameter. What is the volume of the space remaining in the cylinder? Volume of each ball is 4/3 ?r^3 V = 4/3 * 3.1415 * 2^3 V = 1.33 * 3.1415 * 8 = 33.41 cubic inches The volume of 3 balls is: V = 3(33.41) V = 100.23 Volume of the cylinder is area of circle times height: V = 3.14 * 2 * 2 * 1 = 150.72 Volume of remaining space is: V = Volume of cylinder - Volume of 3 balls V = 150.72 - 100.23 V = [B]50.49[/B]

thrice the sum of x y and z The sum of x, y, and z x + y + z Thrice the sum means multiply by 3 [B]3(x + y + z)[/B]

thrice the sum of x y and z The sum of x, y, and z means we add all 3 variables together: x + y + z The word [I]thrice[/I] means we multiply the sum of x, y, and z by 3: 3(x + y +z)

thrice the sum of x y and z The sum of x, y, and z: x + y + z Thrice means multiply the sum by 3: [B]3(x + y + z)[/B]

Let h be the number of hours that pass when Charlie starts. We have the following equations: [LIST] [*]Charlie: D = 40h + 9 [*]Danny: D = 55h [/LIST] Set them equal to each other: 40h + 9 = 55h Subtract 40h from both sides: 15h = 9 h = 3/5 [B]3/5 of an hour = 3(60)/5 = 36 minutes[/B]

Thank you so much [QUOTE="math_celebrity, post: 1003, member: 1"]Let h be the number of hours that pass when Charlie starts. We have the following equations: [LIST] [*]Charlie: D = 40h + 9 [*]Danny: D = 55h [/LIST] Set them equal to each other: 40h + 9 = 55h Subtract 40h from both sides: 15h = 9 h = 3/5 [B]3/5 of an hour = 3(60)/5 = 36 minutes[/B][/QUOTE]

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To be a member of world fitness gym, it costs $60 flat fee and $30 per month. Maria has paid a total of $210 for her gym membership so far. How long has Maria been a member to the gym? The cost function C(m) where m is the number of months for the gym membership is: C(m) = 30m + 60 We're given that C(m) = 210 for Maria. We want to know the number of months (m) that Maria has been a member. With C(m) = 210, we have: 30m + 60 =210 To solve this equation, [URL=' type it in our search engine[/URL] and we get: m = [B]5[/B]

To create an entry code, you must first choose 2 letters and then, 4 single-digit numbers. How many different entry codes can you create? List total combinations using the product of all possibilities: 26 letters (A - Z) * 26 letters (A - Z) * 10 digits (0-9) * 10 digits (0-9) * 10 digits (0-9) * 10 digits (0-9) [B]6,760,000 entry codes [MEDIA=youtube]Y23EGnVuU7I[/MEDIA][/B]

To make an international telephone call, you need the code for the country you are calling. The code for country A, country B, and C are three consecutive integers whose sum is 90. Find the code for each country. If they are three consecutive integers, then we have: [LIST=1] [*]B = A + 1 [*]C = B + 1, which means C = A + 2 [*]A + B + C = 90 [/LIST] Substitute (1) and (2) into (3) A + (A + 1) + (A + 2) = 90 Combine like terms 3A + 3 = 90 Using our [URL=' calculator[/URL], we get: [B]A = 29[/B] Which means: [LIST] [*]B = A + 1 [*]B = 29 + 1 [*][B]B = 30[/B] [*]C = A + 2 [*]C = 29 + 2 [*][B]C = 31[/B] [/LIST] So we have [B](A, B, C) = (29, 30, 31)[/B]

To rent a car it costs $12 per day and $0.50 per kilometer traveled. If a car were rented for 5 days and the charge was $110.00, how many kilometers was the car driven? Using days as d and kilometers as k, we have our cost equation: Rental Charge = $12d + 0.5k We're given Rental Charge = 110 and d = 5, so we plug this in: 110 = 12(5) + 0.5k 110 = 60 + 0.5k [URL=' this into our equation calculator[/URL], we get: [B]k = 100[/B]

To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional pound. To ship a package with FedEx, the cost will be $5 for the first pound and $0.30 for each additional pound. How many pounds will it take for UPS and FedEx to cost the same? If you needed to ship a package that weighs 8 lbs, which shipping company would you choose and how much would you pay? [U]UPS: Set up the cost function C(p) where p is the number of pounds:[/U] C(p) = Number of pounds over 1 * cost per pounds + first pound C(p) = 0.2(p - 1) + 7 [U]FedEx: Set up the cost function C(p) where p is the number of pounds:[/U] C(p) = Number of pounds over 1 * cost per pounds + first pound C(p) = 0.3(p - 1) + 5 [U]When will the costs equal each other? Set the cost functions equal to each other:[/U] 0.2(p - 1) + 7 = 0.3(p - 1) + 5 0.2p - 0.2 + 7 = 0.3p - 0.3 + 5 0.2p + 6.8 = 0.3p + 4.7 To solve this equation for p, we [URL=' it in our search engine[/URL] and we get: p = [B]21 So at 21 pounds, both UPS and FedEx costs are equal [/B] Now, find out which shipping company has a better rate at 8 pounds: [U]UPS:[/U] C(8) = 0.2(8 - 1) + 7 C(8) = 0.2(7) + 7 C(8) = 1.4 + 7 C(8) = 8.4 [U]FedEx:[/U] C(8) = 0.3(8 - 1) + 5 C(8) = 0.3(7) + 5 C(8) = 2.1 + 5 C(8) = [B]7.1[/B] [B]Therefore, FedEx is the better cost at 8 pounds since the cost is lower[/B] [B][/B]

Today a car is valued at $42000. the value is expected to decrease at a rate of 8% each year. what is the value of the car expected to be 6 years from now. Depreciation at 8% per year means it retains (100% - 8%) = 92% of it's value. We set up our depreciation function D(t), where t is the number of years from right now. D(t) = $42,000(0.92)^t The problem asks for D(6): D(6) = $42,000(0.92)^6 D(6) = $42,000(0.606355) D(6) = [B]$25,466.91[/B]

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now. Given that my age is an integer number of years, what is the smallest my age could be? Let my current age be a. We're given: 4/5a > 3/4(a + 1) Multiply through on the right side: 4a/5 > 3a/4 + 3/4 Let's remove fractions by multiply through by 5: 5(4a/5) > 5(3a/4) + 5(3/4) 4a > 15a/4 + 15/4 Now let's remove the other fractions by multiply through by 4: 4(4a) > 4(15a/4) + 4(15/4) 16a > 15a + 15 [URL=' this inequality into our search engine[/URL], we get: a > 15 This means the smallest [I]integer age[/I] which the problem asks for is: 15 + 1 = [B]16[/B]

Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtract 2, the sum is 20. How old is Bill? Let t be Tom's age., s be Sue's age, and b be Bill's age. We have the following equations: [LIST=1] [*]t = s + 2 [*]b = 2t [*]s + t + b - 2 = 20 [/LIST] Get (2) in terms of s (2) b = 2(s + 2) <-- using (1), substitute for t So we have (3) rewritten with substitution as: s + (s + 2) + 2(s + 2) - 2 = 20 s + (s + 2) + 2s + 4 - 2 = 20 Group like terms: (s + s + 2s) + (2 + 4 - 2) = 20 4s + 4 = 20 Run this through our [URL=' calculator [/URL]to get s = 4 Above, we had b = 2(s + 2) Substituting s = 4, we get: 2(4 + 2) = 2(6) = [B]12 Bill is 12 years old[/B]

Translate and solve: 30 times m is greater than ?330. (Write your solution in interval notation.) 30 times m: 30m is greater than -330 30m > -330 Using our [URL=' and interval solver[/URL], we get: m > -11

Free Triangle Inequality Calculator - This calculator displays 2 scenarios1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

Triangle KLM has vertices at . k(-2,-2), l(10,-2), m(4,4) What type of triangle is KLM? [URL=' 1: KL[/URL] = 12 [URL=' 2: LM[/URL] = 8.4853 [URL=' 3: KM[/URL] = 6.3246 Then, we want to find the type of triangle. Using our [URL=' solver with our 3 sides[/URL], we get: [B]Obtuse, Scalene[/B]

Free Trig Measurement Calculator - Given an angle θ, this calculates the following measurements:Sin(θ) = SineCos(θ) = CosineTan(θ) = TangentCsc(θ) = CosecantSec(θ) = SecantCot(θ) = CotangentArcsin(x) = θ = ArcsineArccos(x) = θ = ArccosineArctan(x) =θ = ArctangentAlso converts between Degrees and Radians and Gradians Coterminal Angles as well as determine if it is acute, obtuse, or right angle. For acute angles, a cofunction will be determined. Also shows the trigonometry function unit circle

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triple h then raise the result to the 8th power [U]Triple h means we multiply h by 3:[/U] 3h [U]Raise the result to the 8th power:[/U] [B](3h)^8[/B]

triple s add the result to q then divide what you have by r. Triple s means multiply s by 3: 3s Add the result to q: 3s + q Divide what you have by r: [B](3s + q)/r[/B]

triple the sum of 36 and 6 then add 4 Take this algebraic expression in parts: The sum of 36 and 6: 36 + 6 Triple the sum means we multiply the sum by 3: 3(36 + 6) Then add 4: [B]3(36 + 6) + 4[/B] If the problem asks you to simplify the algebraic expression, we have: 3(42) + 4 126 + 4 [B]130[/B]

The sum of 4 and y is written as (4 + y) Triple that means we multiply that entire sum by 3. 3(4 + y)

The sum of 7 and m is written as 7 + m Triple that means multiply by 3: 3(7 + m)

triple the sum of b and c The sum of b and c b + c Triple this sum 3(b + c)

The sum of y and six is denoted as: y + 6 We triple that sum by multiplying it by 3 3(y + 6)

The difference of a and b is written as: a - b Square the difference means raise the difference to the power of 2 (a - b)^2 Triple this expression means multiply by 3: [B]3(a - b)^2[/B]

Tristan is building a slide for his kids. The ladder is 6 feet tall and the slide is 10 feet long. What is the distance between the ladder and the bottom of the slide? The answer is 8. We have a 3-4-5 triangle. But it's scaled by 2. 3 * 2 = 6 5 * 2 = 10 (hypotenuse-slide) 4 * 2 = [B]8[/B]

True or False (a) The normal distribution curve is always symmetric to its mean. (b) If the variance from a data set is zero, then all the observations in this data set are identical. (c) P(A AND A^c)=1, where A^c is the complement of A. (d) In a hypothesis testing, if the p-value is less than the significance level ?, we do not have sufficient evidence to reject the null hypothesis. (e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set. [B](a) True, it's a bell curve symmetric about the mean (b) True, variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical (c) True. P(A) is the probability of an event and P(Ac) is the complement of the event, or any event that is not A. So either A happens or it does not. It covers all possible events in a sample space. (d) False, we have sufficient evidence to reject H0. (e) False. Volume can be a decimal or fractional. There are multiple values between 127 and 128. So it's continuous.[/B]

Twice a first number decreased by a second number is 16. The first number increased by 3 times the second number is 1. Find the numbers. Let the first number be x and the second number be y. We're given: [LIST=1] [*]2x - y = 16 [*]x + 3y = 1 [/LIST] Using our simultaneous equations calculator, you can solve this 3 ways: [LIST] [*][URL=' Method[/URL] [*][URL=' Method[/URL] [*][URL=' Rule[/URL] [/LIST] No matter what method we use, we get the same answers: [B]x = 7 y = -2 (x, y) = (7, -2) [/B] Let's check our work in equation 1: 2(7) - -2 ? 16 14 + 2 ? 16 16 = 16 <-- Check Let's check our work in equation 2: 7 + 3(-2) ? 1 7 - 6 ? 1 1 = 1 <-- Check

twice a number subtracted from the square root of the same number The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x Twice a number means we multiply x by 2: 2x Square root of the same number: sqrt(x) twice a number subtracted from the square root of the same number [B]sqrt(x) - 2x[/B]

twice the difference between x and 28 is 3 times a number The difference between x and 28: x - 28 Twice the difference means we multiply x - 28 by 2: 2(x - 28) The phrase [I]a number[/I] means an arbitrary variable, let's call it x x 3 times a number: 3x The word [I]is[/I] means equal to, so we set 2(x - 28) equal to 3x: [B]2(x - 28) = 3x[/B]

twice the difference of a number and 3 is equal to 3 times the sum of a number and 2. We've got 2 algebraic expressions here. Let's take them in parts. Left side algebraic expression: twice the difference of a number and 3 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]The word [I]difference[/I] means we subtract 3 from the variable x [*]x - 3 [*]Twice this difference means we multiply (x - 3) by 2 [*]2(x - 3) [/LIST] Right side algebraic expression: 3 times the sum of a number and 2 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]The word [I]sum[/I] means we add 2 to the variable x [*]x + 2 [*]3 times the sum means we multiply (x + 2) by 3 [*]3(x + 2) [/LIST] Now, we have both algebraic expressions, the problem says [I]is equal to[/I] This means we have an equation, where we set the left side algebraic expression equal to the right side algebraic expression using the equal sign (=) to get our answer [B]2(x - 3) = 3(x + 2)[/B]

twice the difference of a number and 55 is equal to 3 times the sum of a number and 8 Take this algebraic expression in pieces. Left side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The difference of this number and 55 means we subtract 55 from x x - 55 Twice the difference means we multiply x - 55 by 2 2(x - 55) Right side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The sum of a number and 8 means we add 8 to x x + 8 3 times the sum means we multiply x + 8 by 3 3(x + 8) Now that we have the left and right side of the expressions, we see the phrase [I]is equal to[/I]. This means an equation, so we set the left side equal to the right side: [B]2(x - 55) = 3(x + 8)[/B]

seven plus x 7 + x Twice the quantity of seven plus x 2(7 + x) Difference of x and seven x - 7 The phrase [I]is the same as[/I] means equal to. This is our algebraic expression: [B]2(7 + x) = x - 7 [/B] If the problem asks you to solve for x, distribute 2 on the left side: 14 + 2x = x - 7 Subtract x from the right side 14 + x = -7 Subtract 14 from each side [B]x = -21[/B]

two y and six 2y + 6 Twice the quantity: [B]2(2y + 6)[/B]

twice the square of the product of x and y Take this algebraic expression in pieces: [LIST] [*]The product of x and y means we multiply x and y: xy [*]The square of the product means we raise xy to the power of 2: (xy)^2 = x^2y^2 [*]Twice the square means we multiply the square by 2: [B]2x^2y^2[/B] [/LIST]

twice the square of the product of x and y [LIST] [*]The product of x and y: xy [*]The square of the product means we raise xy to the power of 2: (xy)^2 [*]Twice the square means we multiply by 2 [/LIST] [B]2(xy)^2 or 2x^2y^2[/B]

twice the square root of a number increased by 5 is 23 The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x The square root of a number means we raise x to the 1/2 power: sqrt(x) the square root of a number increased by 5 means we add 5 to sqrt(x): sqrt(x) + 5 twice the square root of a number increased by 5 means we multiply sqrt(x) + 5 by 2: 2(sqrt(x) + 5) The phrase [I]is 23[/I] means we set 2(sqrt(x) + 5) equal to 23: [B]2(sqrt(x) + 5) = 23[/B]

twice the sum of a and b is thrice c The sum of a and b: a + b twice the sum of a and b means we multiply the sum of a and b by 2: 2(a + b) Thrice c means we multiply c by 3: 3c The word [I]is[/I] means equal to, so we set 2(a + b) equal to 3c: [B]2(a + b) = 3c [MEDIA=youtube]G_D4b8Jv89Q[/MEDIA][/B]

[SIZE=6]Twice the sum of a number and 6 is equal to three times the difference of the number and 3. Find the number. The phrase [/SIZE][I][SIZE=7]a number[/SIZE][/I][SIZE=6] means an arbitrary variable, let's call it x. The sum of a number and 6 means we add 6 to x: x + 6 Twice the sum of a number and 6 means we multiply x + 6 by 2: 2(x + 6) the difference of the number and 3 means we subtract 3 from x x - 3 three times the difference of the number and 3 means we multiply x - 3 by 3: 3(x- 3) The word [I]is[/I] means we set 2(x + 6) equal to 3(x - 3) 2(x + 6) = 3(x - 3) Use the distributive property to multiply through: 2x + 12 = 3x - 9 Subtract 2x from each side: 2x - 2x + 12 = 3x - 2x - 9 x - 9 = 12 Add 9 to each side: x - 9 + 9 = 12 + 9 x = [B]21[/B] [B][/B] [B][MEDIA=youtube]CeZl_oZnSiw[/MEDIA][/B][/SIZE]

Two consecutive even integers that equal 126 Let the first integer equal x. So the next even integer must be x + 2. The sum which is equal to 126 is written as x + (x + 2) = 126 Simplify: 2x + 2 = 126 Using our [URL=' calculator,[/URL] we get: x = 62 This means the next consecutive even integer is 62 = 2 = 64. So our two even consecutive integers with a sum of 126 are [B](62, 64)[/B]

Two fifths of the sum of 8 and b The sum of 8 and b 8 + b Two fifths of this sum: [B]2/5(8 + b)[/B]

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of 1225. what was the rate charged per hour by each mechanic if the sum of the two rates was 170 per hour? Set up two equations: (1) 10x + 5y = 1225 (2) x + y = 170 Rearrange (2) x = 170 - y Substitute that into (1) 10(170 - y) + 5y = 1225 1700 - 10y + 5y = 1225 1700 - 5y = 1225 Move 5y to the other side 5y + 1225 = 1700 Subtract 1225 from each side 5y =475 Divide each side by 5 [B]y = 95[/B] Which means x = 170 - 95, [B]x = 75[/B]

2h/9 or (2/9)h

Two numbers have a sum of 20. Determine the lowest possible sum of their squares. If sum of two numbers is 20, let one number be x. Then the other number would be 20 - x. The sum of their squares is: x^2+(20 - x)^2 Expand this and we get: x^2 + 400 - 40x + x^2 Combine like terms: 2x^2 - 40x + 400 Rewrite this: 2(x^2 - 20x + 100 - 100) + 400 2(x - 10)^2 - 200 + 400 2(x?10)^2 + 200 The sum of squares of two numbers is sum of two positive numbers, one of which is a constant of 200. The other number, 2(x - 10)^2, can change according to the value of x. The least value could be 0, when x=10 Therefore, the minimum value of sum of squares of two numbers is 0 + 200 = 200 when x = 10. If x = 10, then the other number is 20 - 10 = 10.

Two numbers have a sum of 59. If one number is q, express the other number on terms of q The other number is [B]59 - q[/B]. Add them together, you get q + (59 - q) = 59.

two numbers have an average of 2100 and one number is $425 more than the other number. What are the numbers Let the first number be x and the second number be y. We're given two equations: [LIST=1] [*](x + y)/2 = 2100 (Average) [*]y = x + 425 [/LIST] Rearrange equation (1) by cross multiplying x + y = 2 * 2100 x + y = 4200 So we have our revised set of equations: [LIST=1] [*]x + y = 4200 [*]y = x + 425 [/LIST] Substituting equation (2) into equation (1) for y, we get: x + (x + 425) = 4200 Combining like terms, we get: 2x + 425 = 4200 Using our [URL=' solver[/URL], we get: x = [B]1887.5[/B] Which means using equation (2), we get y = 1887.5 + 425 y = [B]2312.5[/B]

Two numbers have the sum of 40 if one number is P express the other in terms of P We write this as P + (40 - P) = 40 So the other number is [B]40 - P[/B]

Two numbers that total 44 and have a difference of 6. Let the two numbers be x and y. We're given the following equations: [LIST=1] [*]x + y = 44 <-- Total means a sum [*]x - y = 6 [/LIST] Add the two equations together: (x + x) + (y - y) = 44 + 6 Cancelling the y terms, we have: 2x = 50 [URL=' this equation into the search engine[/URL], we get: [B]x = 25 [/B] Rearranging equation (2) above, we get: y = x - 6 Substituting x = 25 into this, we get: y = 25 - 6 [B]y = 19[/B]

Two numbers total 12, and their differences is 20. Find the two numbers. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x + y = 12 [*]x - y = 20 [/LIST] Since we have y coefficients of (-1 and 1) that cancel, we add the two equations together: (x + x) + (y - y) = 12 + 20 The y terms cancel, so we have: 2x = 32 [URL=' this equation into our search engine[/URL] and we get: x = [B]16[/B] Substitute this value of x = 16 back into equation 1: 16 + y = 12 [URL=' this equation into our search engine[/URL], we get: y = [B]-4 [/B] Now, let's check our work for both equations: [LIST=1] [*]16 - 4 = 12 [*]16 - -4 --> 16 + 4 = 20 [/LIST] So these both check out. (x, y) = ([B]16, -4)[/B]

Two numbers total 50 and have a difference of 28. Find the two numbers. Using x and y as our two numbers, we write the following 2 equations: [LIST=1] [*]x + y = 50 [*]x - y = 28 [/LIST] Add the 2 rows: 2x = 78 Divide each side by 2: [B]x = 39[/B] If x = 39, then from (1), we have y = 50 - 39 [B]y = 11[/B]

Let the numbers be x and y. Set up our givens: [LIST=1] [*]x + y = 83 [*]x - y = 17 [/LIST] [U]Add equation (1) to equation (2)[/U] x + x + y - y = 83 + 17 [U]The y-terms cancel out:[/U] 2x = 100 [U]Divide each side by 2:[/U] 2x/2= 100/2 x = [B]50[/B] [U] Plug x = 50 into equation (1)[/U] 50 + y = 83 [U]Subtract 50 from each side:[/U] 50 - 50 + y = 83 - 50 [U]Cancel the 50 on the left side:[/U] y = [B]33 [/B] So our two numbers (x, y) = (33, 50) [MEDIA=youtube]jajO043ChUM[/MEDIA]

The sum of p and 2 is written as p + 2. 2/3 of the sum is written as: 2(p + 2) --------- 3

two unbiased dice are thrown. find the probability that the total number on the dice is greater than 10 [URL=' our 2 dice calculator[/URL]: We have (5,6),(6,5),(6,6) P(Sum) > 10 is [B]1/12[/B]

two-thirds the difference of c and d The difference of c and d: c - d two-thirds the difference means we multiply c - d by 2/3: [B]2(c - d)/3[/B]

Tyler has a meal account with $1200 in it to start the school year. Each week he spends $21 on food a.) write an equation that relates the amount in the account (a) with the number of (w) weeks b.) How many weeks will it take until Tyler runs out of money? [U]Part a) where w is the number of weeks[/U] a = Initial account value - weekly spend * w ([I]we subtract because Tyler spends)[/I] a = [B]1200 - 21w [/B] [U]Part b)[/U] We want to know the number of weeks it takes where a = 0. So we have: 1200 - 21w = 0 To solve for w, we [URL=' this equation into our search engine[/URL] and we get: w = 57.14 weeks The problem asks for when he runs out of money, so we round up to [B]58 whole weeks[/B]

Free Uniform Distribution Calculator - This calculates the following items for a uniform distribution* Probability Density Function (PDF) ƒ(x) * Cumulative Distribution Function (CDF) F(x) * Mean, Variance, and Standard Deviation Calculates moment number t using the moment generating function

Free Units of Output (Service Output) Depreciation Calculator - Given an asset value, salvage value, production units, and units per period, this calculates the depreciation per period using the units of output depreciation (service output depreciation)

Use k as the constant of variation. L varies jointly as u and the square root of v. Since u and v vary jointly, we multiply by the constant of variation k: [B]l = ku * sqrt(v)[/B]

Use number 7,6,5 and 3 only one time to get 75 We do it using this order of operations: [B](7 + 5) * 6 + 3[/B] Simplifying, we get: 12*6 + 3 72 + 3 75

Use the definite integral to find the area between the x-axis and the function f(x)= x^2-x-12 over the interval [ -5, 10]. Using our [URL=' calculator[/URL], we get: [B]157.5[/B]

Use the information below to determine the weight of 500 gallons of water. a) There are 1.057 quarts in a liter and 4 quarts in a gallon b) A cubic decimeter of water is a liter of water c) A cubic decimeter of water weighs one kilogram d) There are 2.2 pounds in a kilogram [LIST] [*]500 gallons = 2000 quarts [*]2000 quarts / 1.057 quarts in a liter = 1892.15 liters [*]1892.15 liters weight 1892.15 kilograms [*]1892.15 kilograms x 2.2 pounds = [B]4163 pounds[/B] [/LIST]

v is equal to the product of 7 and the sum of u and 6 [LIST] [*]Sum of u and 6: u + 6 [*]the product of 7 and the sum of u and 6: 7(u + 6) [*]We set this expression equal to v: [/LIST] [B]v = 7(u + 6)[/B]

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that starts with 13 and continues to add seven to each output. For now, van needs to know what the 15th output will be. Complete the steps needed to determine the 15th term in sequence. Given a first term a1 of 13 and a change amount of 7, expand the series The explicit formula for an [I]arithmetic series[/I] is an = a1 + (n - 1)d d represents the common difference between each term, an - an - 1 Looking at all the terms, we see the common difference is 7, and we have a1 = 13 Therefore, our explicit formula is an = 13 + 7(n - 1) If n = 15, then we plug it into our explicit formula above: an = 13 + 7(n - 1) a(15) = 15 + 7(15 - 1) a(15) = 15 + 7 * 14 a(15) = 15 + 98 a(15) = [B]113[/B]

Free Vectors Calculator - Given 2 vectors A and B, this calculates:* Length (magnitude) of A = ||A||* Length (magnitude) of B = ||B||* Sum of A and B = A + B (addition)* Difference of A and B = A - B (subtraction)* Dot Product of vectors A and B = A x BA ÷ B (division)* Distance between A and B = AB* Angle between A and B = θ* Unit Vector U of A.* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).* Cauchy-Schwarz Inequality* The orthogonal projection of A on to B, proj_BA and and the vector component of A orthogonal to B → A - proj_BA Also calculates the horizontal component and vertical component of a 2-D vector.

Free Venn Diagram (2 circles) Calculator - Given two circles A and B with an intersection piece of C, this will calculate all relevant probabilities of the Venn Diagram.

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years. Let Victoria's age be v. And her neighbor's age be n. We're given: [LIST=1] [*]v = n + 4 [*]v + n <=14 <-- no more than means less than or equal to [/LIST] Substitute Equation (1) into Inequality (2): (n + 4) + n <= 14 Combine like terms: 2n + 4 <= 14 [URL=' this inequality into our search engine[/URL], we get: n <= 5 Substituting this into inequality (2): v + 5 <= 14 [URL=' this inequality into our search engine[/URL], we get: [B]v <= 9[/B]

vw^2+y=x for w This is an algebraic expression. Subtract y from each side: vw^2 + y - y = x - y The y's cancel on the left side, so we're left with: vw^2 = x - y Divide each side by v w^2 = (x - y)/v Take the square root of each side: w = [B]Sqrt((x - y)/v)[/B]

Free Walking Distance (Pedometer) Calculator - Given a number of steps and a distance per stride in feet, this calculator will determine how far you walk in other linear measurements.

Wan bought 2 salad rolls and 1 bottle of orange juice. If each salad roll costs x cents and the orange juice costs $1.50, write the expression for the total cost (in cents) for the food and drink The cost C is: C = 2x + 1.50(1) Simplify: [B]C = 2x + 1.50[/B]

Waynes widget world sells widgets to stores for $10.20 each (wholesale price). A local store marks them up $6.79. What is the retail price at this store? [I]Note: Markup means we add to the wholesale price. [/I] Calculate Retail Price: Retail Price = Wholesale Price + Markup Amount Retail Price = $10.20 + $6.79 Retail Price = [B]$16.99[/B]

Free Weight Conversions Calculator - This calculator converts between the following weight measurements: * Ounces (oz.) * Pounds (lb.) * Tons * Milligrams (mg.) * Grams * Kilograms (kg.) * Centigrams (cg.) * Micrograms (mcg.) * Stone

Free Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM) Calculator - Calculates the Weighted Average Cost of Capital (WACC) and also calculates the return on equity if not given using the Capital Asset Pricing Model (CAPM) using debt and other inputs such as Beta and risk free rate.

What can we conclude if the coefficient of determination is 0.94? [LIST] [*]Strength of relationship is 0.94 [*]Direction of relationship is positive [*]94% of total variation of one variable(y) is explained by variation in the other variable(x). [*]All of the above are correct [/LIST] [B]94% of total variation of one variable(y) is explained by variation in the other variable(x)[/B]. The coefficient of determination explains ratio of explained variation to the total variation.

What does y=f(x) mean It means y = a function of the variable x. x is the independent variable and y is the dependent variable. f(x) means a function in terms of x

What fraction lies exactly halfway between 2/3 and 3/4? A) 3/5 B) 5/6 C) 7/12 D) 9/16 E) 17/24 Halfway means taking the average, which is dividing the sum of the fractions by 2 for 2 fractions: 1/2(2/3 + 3/4) 1/2(2/3) + 1/2(3/4) 1/3 + 3/8 We need common denominators, so [URL=' type this fraction sum into our search engine[/URL] and get: [B]17/24 - Answer E[/B]

Map this out as a function with term number n and value 1, 0 2, 7 3, 14 4, 21 The values jump by 7, but they do so as the n - 1 term. We have the series formula S(n) = 7(n - 1) The problem asks for S(1000) S(1000) = 7(1000 - 1) S(1000) = 7(999) S(1000) = [B]6,993[/B] [MEDIA=youtube]ZF10Ec29XKo[/MEDIA]

What is the 7th number in the following pattern: 3.2, 4.4, 5.6, 6.8, ... This is an arithmetic sequence with an increase amount of 1.2. Each term S(n) is found by adding 1.2 to the prior term. S(1) = 3.2 S(2) = 3.2 + 1.2 = 4.4 S(3) = 4.4 + 1.2 = 5.6 S(4) = 5.6 + 1.2 = 6.8 S(5) = 6.8 + 1.2 = 8.0 S(6) = 8.0 + 1.2 = 9.2 S(7) = 9.2 + 1.2 = [B]10.4[/B]

What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.4%? Round to three decimal places. Use a 365 day year. [U]Set up the accumulation equation:[/U] (1+i)^365 = 1.054 [U]Take the natural log of each side[/U] 365 * Ln(1 + i) = 1.054 Ln(1 + i) = 0.000144089 [U]Use each side as a exponent to eulers constant e[/U] (1 + i) = e^0.000144089 1 + i = 1.000144099 i = 0.000144099 or [B].0144099%[/B]

What is the area of a triangular parking lot with a width of 200m and a length of 100m? Area of a Triangle = bh/2 Plugging in our numbers, we get: Area of Parking Lot = 200(100)/2 Area of Parking Lot = 100 * 100 Area of Parking Lot = [B]10,000 sq meters[/B]

What is the average of 7 consecutive numbers if the smallest number is called n? [LIST] [*]First number = n [*]Second number = n + 1 [*]Third number = n + 2 [*]Fourth number = n + 3 [*]Fifth number = n + 4 [*]Sixth number = n + 5 [*]Seventh number = n + 6 [/LIST] Average = Sum of all numbers / Total numbers Average = (n + n + 1 + n + 2 + n + 3 + n + 4 + n + 5 + n + 6)/7 Average = 7n + 21/7 Factor out a 7 from the top: 7(n + 3)/7 Cancel the 7's: [B]n + 3[/B]

What is the formula for the area of a circle? Given a radius r, we have Area (A) of: [B]A = ?r^2[/B]

What is the formula for the volume of a cylinder? The Volume (V) of a cylinder with radius (r) and height (h) is: [B]V = ?r^2h[/B]

The only way you can roll a 12 with two dice is 6 and 6. Since each die roll is independent, we have: [LIST] [*]P(12) = P(6) * P(6) [*]P(12) = 1/6 * 1/6 [*]P(12) = 1/36. [/LIST] Now, what is the probability we roll a 12 five times in a row? The same rules apply, each new roll is independent of the last, so we multiply: [LIST] [*]P(12, 12, 12, 12, 12) = 1/36 * 1/36 * 1/36 * 1/36 * /36 [*]P(12, 12, 12, 12, 12) = [B]1/60,466,176[/B] or [B]1.65381717e-8[/B] [/LIST]

what is the probabilty of tossing two coins and both landing on heads We want P(HH). We type in [URL=' into our search engine[/URL] and we get: P(HH) = [B]0.25 or 1/4[/B]

What is the ratio of the area of a circle to the area of a square drawn around that circle? Express your answer in terms of pi. Area of a circle = pir^2 area of a square = (2r)^2 = 4r^2 Ratio = pir^2/4r^2 Ratio = [B]pi/4[/B]

What is the ratio of vowels to consonants in the word RAINBOW Vowels (3): A, I, O Consonants (4): R, N, B, W Ratio of vowels to consonants: [B]3:4[/B]

What is the slope of the line through (1,9) and (5,3) [URL=' run this through our slope calculator[/URL], and get an initial slope of 6/4. But this is not in simplest form. So we type 6/4 into our calculator, and s[URL=' the simplify option[/URL]. We get [B]3/2[/B]

What is the sum of a number x and y raised to the power of two in an algebraic expression? The sum of a number x and y: x + y Raise this to the power of 2 (x + y)^2

What is the sum of four consecutive multiples of 5? First number = n Second number = n + 5 Third number = n + 10 Fourth number = n + 15 Add them together: (n + n + n + n) + (5 + 10 + 15) [B]4n + 30[/B]

What is the X coordinate of the point (6, 19) Using our [URL=' pair calculator[/URL], we see that the x coordinate is [B]6[/B]

What pair of consecutive integers gives the following: 7 times the smaller is less than 6 times the larger? Let x and y be consecutive integers, where y = x + 1 We have 7x < 6y as our inequality. Substituting x, y = x + 1, we have: 7x < 6(x + 1) 7x < 6x + 6 Subtracting x from each side, we have: x < 6, so y = 6 + 1 = 7 (x, y) = (6, 7)

What pair of factors of -28 has a sum of -3? We type in [I]factor -28[/I] into our search engine. Scrolling down the list of factor sums, we see: -7 + 4 = -3 So our answer is [B](-7, 4)[/B]

what two values can d have if d squared is 9 d^2 = 9 Using [URL='(9%2F1)&pl=Simplify+Radical+Expression']our calculator[/URL], we get: d = [B](-3, 3}[/B]

whats the probability of rolling a 5 and then rolling a number less then 2 [U]Roll a 5:[/U] There's only one 5 on a six sided die P(X = 5) = 1/6 A number less than 2 is only 1: P(X < 2) = P(X = 1) P(X = 1) = 1/6 Since each event is independent, we multiply: P(X = 5) * P(X = 1) = 1/6 * 1/6 P(X = 5) * P(X = 1) = [B]1/36[/B]

When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negative solution. Let the number be n. Square of a number: n^2 28 is subtracted from the square of a number: n^2 - 28 3 times the number: 3n [I]The result is[/I] mean an equation, so we set n^2 - 28 = 3n n^2 - 28 = 3n Subtract 3n from each side: n^2 - 3n - 28 = 3n - 3n The right side cancels to 0, so we have: n^2 - 3n - 28 = 0 This is a quadratic equation in standard form, so we [URL=' our quadratic calculator[/URL] to solve: We get two solutions for n: n = (-4, 7) The question asks for the negative solution, so our answer is: [B]n = -4[/B]

When 3 consecutive positive integers are multiplied, the product is 16 times the sum of the 3 integers. What is the difference of the product minus the sum? Let the 3 consecutive positive integers be: [LIST=1] [*]x [*]x + 1 [*]x + 2 [/LIST] The product is: x(x + 1)(x + 2) The sum is: x + x + 1 + x + 2 = 3x + 3 We're told the product is equivalent to: x(x + 1)(x + 2) = 16(3x + 3) x(x + 1)(x + 2) = 16 * 3(x + 1) Divide each side by (x + 1) x(x + 2) = 48 x^2 + 2x = 48 x^2 + 2x - 48 = 0 Now subtract the sum from the product: x^2 + 2x - 48 - (3x + 3) [B]x^2 - x - 51[/B]

When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unknown number. Write the translated equation below. [LIST=1] [*]39 added to a number is written as n + 39 [*]40 times the number is written as 40n [*]The result is means we have an equation, so set (1) equal to (2) [/LIST] n+ 39 = 40n Running [URL=' + 39 = 40n through the search engine[/URL], we get[B] n = 1[/B].

When 4 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution. Let the number be n. We have: n^2 - 4 = 3n Subtract 3n from each side: n^2 - 3n - 4 = 0 [URL=' this quadratic equation into the search engine[/URL], we get: n = (-1, 4) The problem asks for the positive solution, so we get [B]n = 4[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 4 times a number means we multiply x by 4: 4x Increased by 40 means we add 40 to 4x: 4x + 40 100 decreased by the number means we subtract x from 100: 100 - x The phrase [I]is the same as[/I] means equal to, so we set 4x + 40 equal to 100 - x 4x + 40 = 100 - x Solve for [I]x[/I] in the equation 4x + 40 = 100 - x [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4x and -x. To do that, we add x to both sides 4x + 40 + x = -x + 100 + x [SIZE=5][B]Step 2: Cancel -x on the right side:[/B][/SIZE] 5x + 40 = 100 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 40 and 100. To do that, we subtract 40 from both sides 5x + 40 - 40 = 100 - 40 [SIZE=5][B]Step 4: Cancel 40 on the left side:[/B][/SIZE] 5x = 60 [SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE] 5x/5 = 60/5 x = [B]12[/B] Check our work for x = 12: 4(12) + 40 ? 100 - 12 48 + 40 ? 100 - 12 88 = 88

When a circle's radius triples, what happens to its area? A = ?r^2 When r = 3r, then we have: a = ?(3r)^2 A = 9(?r^2) This means Area increases by [B]9x [MEDIA=youtube]j5aqShSh4uE[/MEDIA][/B]

When a dog noticed a fox, they were 60 meters apart. The dog immediately started to chase the fox at a speed of 750 meters per minute. The fox started to run away at a speed of 720 meters per minute. How soon will the dog catch the fox? The dog sits a position p. Distance = Rate x Time The dogs distance in minutes is D = 720t The fox sits at position p + 60 Distance = Rate x Time The fox's distance in minutes is D = 750t - 60 <-- Subtract 60 since the fox is already ahead 60 meters. We want to know when their distance (location) is the same. So we set both distance equations equal to each other: 720t = 750t - 60 [URL=' our equation calculator[/URL], we get [B]t = 2[/B]. Let's check our work: Dog's distance is 720(2) = 1440 Fox's distance is 750(2) - 60 = 1,440

When finding the power of a power, you _____________________ the exponents [B]Multiply [/B] Example: (a^b)^c = a^bc

When five people are playing a game called hearts, each person is dealt ten cards and the two remaining cards are put face down on a table. Because of the rules of the game, it is very important to know the probability of either of the two cards being a heart. What is the probability that at least one card is a heart? Probability that first card is not a heart is 3/4 since 4 suits in the deck, hearts are 1/4 of the deck. Since we don't replace cards, the probability of the next card drawn without a heart is (13*3 - 1)/51 = 38/51 Probability of both cards not being hearts is found by multiplying both individual probabilities: 3/4 * 38/51 = 114/204 Having at least one heart is found by subtracting this from 1 which is 204/204: 204/204 - 114/204 = 90/204 [URL=' reduces to[/URL] [B]15/34[/B]

When Mike uses a riding mower, it takes him 3 hours to mow his lawn. When he uses a push mower, it takes him 6 hours to mow the lawn. (His sister also can mow the lawn with the push mower in 6 hours.). Mike wanted to get the lawn mowed as quickly as possible, so he paid his sister $10 to mow with the push mower while he used the riding mower. How long will it take Mike an his sister to mow the lawn if they worked together? Mike can mow 1/3 of the lawn in an hour. Mike's sister can mow 1/6 the lawn in an hour. together, they can mow [URL=' + 1/6 [/URL]= 1/2 of the lawn in one hour. Which means it would take [B]2 hours [/B](2 * 1/2) = 1 to mow the full lawn.

When ringing up a customer, a cashier needs 3 seconds to scan each item and 9 seconds to process the payment. Let m represent the number of items and s represent the number of seconds to ring up a customer. Build our equation R(m): [B]R(m) = ms + 9[/B]

When the side of a square is doubled in length, its area increases by 432 square inches. What is the size of the original square? Original square side length is s Area = s^2 Double the side lengths to 2s New area = (2s)^2 = 4s^2 Setup the difference relation: 4s^2 - s^2 = 432 3s^2 = 432 Divide each side by 3: 3s^2/3 = 432/3 s^2 = 144 s = [B]12[/B]

Which of the following descriptions of confidence interval is correct? (Select all that apply) a. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0 b. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0 c. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1 d. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1 [B]a. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0 c. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1 [/B] [I]The lower the confidence interval, the wider the range, so if a higher confidence interval contains a point, a lower confidence interval will contain that point as well.[/I]

Which of the following descriptions of null hypothesis are correct? (Select all that apply) a. A null hypothesis is a hypothesis tested in significance testing. b. The parameter of a null hypothesis is commonly 0. c. The aim of all research is to prove the null hypothesis is true d. Researchers can reject the null hypothesis if the P-value is above 0.05 [B]a. A null hypothesis is a hypothesis tested in significance testing. [/B] [I]b. is false because a parameter can be anything we choose it to be c. is false because our aim is to disprove or fail to reject the null hypothesis d. is false since a p-value [U]below[/U] 0.05 is often the rejection level.[/I]

Which of the following equations represents a line that is parallel to the line with equation y = -3x + 4? A) 6x + 2y = 15 B) 3x - y = 7 C) 2x - 3y = 6 D) x + 3y = 1 Parallel lines have the same slope, so we're looking for a line with a slope of 3, in the form y = mx + b. For this case, we want a line with a slope of -3, like our given line. If we rearrange A) by subtracting 6x from each side, we get: 2y = -6x + 15 Divide each side by 2, we get: y = -3x + 15/2 This line is in the form y = mx + b, where m = -3. So our answer is [B]A[/B].

Which of the following is equivalent to 3(2x + 1)(4x + 1)? [LIST] [*]A) 45x [*]B) 24x^2 + 3 [*]C) 24x^2 + 18x + 3 [*]D) 18x^2 + 6 [/LIST] First, [URL=' the binomials[/URL]: We get 8x^2 + 6x + 1 Now multiply this polynomial by 3: 3(8x^2 + 6x + 1) = [B]24x^2 + 18x + 3, answer C[/B]

Which of the following is equivalent to 9^3/4? a) 9^1/3 b) 9 ^ 1/4 c) sqrt(3) d) 3 * sqrt(3) Since 9 is 3^2, we have 3^(3*2/4) which is 3^6/4 Since 6/4 is 3/2, we have: 3^(3/2) Since 3/2 is 1 + 1/2, we have: 3^1*sqrt(3) [B]3*sqrt(3) or option D. [MEDIA=youtube]Uq544xLphiM[/MEDIA][/B]

Which of the following is equivalent to the sum of the expression a^2 - 1 and a + 1? A) a^2 + a B) a^3 - 1 C) 2a^2 D) a^3 a^2 - 1 + a + 1 The 1's cancel, so we're left with: [B]a^2 + a - Answer A[/B]

Which of the following is the probability that a green marble will be selected from a bag containing 9 red marbles 6 blue marbles 7 green marbles and 11 yellow marbles if one is selected randomly? Total marbles in the bag: 9 red + 6 blue + 7 green + 11 yellow = 33 P(Green) = Green Marbles / Total Marbles P(Green) = [B]7/33[/B]

Which of the followings can increase the value of t? (select all the apply) a. Increase the standard deviation of difference scores b. Decrease the standard deviation of difference scores c. Increase the difference between means d. Decrease the difference between means [B]b. Decrease the standard deviation of difference scores c. Increase the difference between means[/B] [I]Increase numerator or decrease denominator of the t-value formula[/I]

Whitney has already baked 2 cakes, and she can bake 1 cake with each additional stick of butter she buys. Write an equation that shows the relationship between the number of additional sticks of butter s and the number of cakes c. [LIST] [*]Let c, the number of cakes, be represented by f(s) where s are the number of sticks of butter. [*]We already have 2 cakes to start, and each additional stick of butter gets us one more cake. [/LIST] f(s) = 1s + 2 Simplify, since 1s is just s [B]f(s) = s + 2[/B]

Wilbie had candy to give to his 3 children. He first took 5 pieces and evenly divided the rest among each child. Each child received 3 pieces. With how many pieces did he start? Let the starting candy amount be c. We're given: (c - 5)/3 = 3 Cross multiply: c - 5 = 3*3 c - 5 = 9 [URL=' this equation into the search engine[/URL], and we get: c = 14

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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Hugo is going to send some flowers to his wife. Somerville Florist charges $2 per rose, plus $39 for the vase. Dwaynes Flowers, in contrast, charges $3 per rose and $10 for the vase. If Hugo orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be? How many roses would there be? Let r be the number of roses and C(r) be the cost function. The vase is a one-time cost. Somerville Florist: C(r) = 2r + 39 Dwaynes Flowers C(r) = 3r + 10 Set them equal to each other: 2r + 39 = 3r + 10 Using our [URL=' calculator[/URL], we get: [B]r = 29[/B]

Write an algebraic expression for 8 multiplied by the result of u reduced by 11. u [I]reduced by[/I] 11 Reduced by means subtract 11 from u. So we have: u - 11 We multiply this expression by 8 to get our algebraic expression of: [B]8(u - 11)[/B]

Write an equation in slope-intercept form for the line with slope 4 and y-intercept -7 The standard equation for slope (m) and y-intercept (b) is given as: y = mx + b We're given m = 4 and y-intercept = -7, so we have: [B]y = 4x - 7[/B]

Write in set builder form {all possible numbers formed by any two of the digits 1 2 5} With 3 numbers, we got [URL=' = 6[/URL] possible numbers formed by the two digits [LIST=1] [*]12 [*]15 [*]21 [*]25 [*]51 [*]52 [/LIST] In set builder notation, we write this as: {x : x ? {12, 15, 21, 25, 51, 52}) x such that x is a element of the set {12, 15, 21, 25, 51, 52}

Write the interval (2,5) in set builder notation It's a closed interval, so [URL=' type in [2,5] into the search engine[/URL], and we get: [B]{x|2<= x <= 5}[/B]

Your answer is correct. Here is how I set up the profit equation where h is the hours worked and x is the supply cost: P(h) = 15.35h + x We know P(4) = 141.73 P(4) = 15.35(4) + x 141.73 = 15.35(4) + x Simplify 141.73 = 61.4 + x Subtract 61.4 from each side: [B]x = 80.33[/B]

wy - ma = ay/n for y Subtract ay/n from each side: wy - ma - ay/n = ay/n - ay/n wy - ma - ay/n = 0 Now add ma to each side: wy - ay/n = ma Factor out y: y(w - a/n) = ma Divide each side by (w - a/n) y = [B]ma/(w - a/n)[/B]

x add y, multiply by z then subtract d Take this algebraic expression in pieces: [LIST] [*]x add y: x + y [*]multiply by z: z(x + y) [*]Subtract d: [B]z(x + y) - d[/B] [/LIST]

X minus 5 plus x equals 79 x minus 5 x - 5 plus x x - 5 + x equals 79 x - 5 + x = 79 Group like terms: (x + x) - 5 = 79 [B]2x - 5 = 79[/B]

x plus y times x minus y Plus means we add. Minus means we subtract. So we have: [B](x + y)(x - y)[/B]

x squared times the difference of x and y x squared means we raise x to the power of 2: x^2 The difference of x and y x - y x squared times the difference of x and y [B]x^2(x - y)[/B]

X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4 Varies directly means there is a constant k such that: x = ky^(1/3) When x = 1 and y = 27, we have: 27^1/3(k) = 1 3k = 1 To solve for k, we[URL=' type in our equation into our search engine[/URL] and we get: k = 1/3 Now, the problem asks for y when x = 4. We use our variation equation above with k = 1/3 and x = 4: 4 = y^(1/3)/3 Cross multiply: y^(1/3) = 4 * 3 y^(1/3) =12 Cube each side: y^(1/3)^3 = 12^3 y = [B]1728[/B]

(X+y)/3=5 for x Cross multiply: x + y = 15 Subtract y from each side: [B]x = 15 - y[/B]

x/3 - g = a for x Add g to each side so we can isolate the x term: x/3 - g + g = a + g Cancel the g terms on the left side and we get: x/3 = a + g Multiply each side by 3 to isolate x: 3(x/3) = 3(a + g) Cancelling the 3's on the left side, we get: x = [B]3(a + g)[/B]

x/5-7=2q for x Add 7 to each side: x/5 -7 + 7 = 2q + 7 Cancel the 7's on the left side, we get: x/5 = 2q + 7 Cross multiply the 5: x = 5(2q + 7) x = [B]10q + 35[/B]

x/r - h = 4 for x Add h to each side: x/r - h + h = h + 4 Cancel the h's on the left side, we get: x/r = h + 4 Multiply each side by r to isolate x: xr/r = r(h + 4) Cancel the r's on the left side, we get: x = [B]r(h + 4)[/B]

x/y + 9 = n for x Subtract 9 from each side to isolate the x term: x/y + 9 - 9 = n - 9 Cancel the 9's on the left side and we get: x/y = n - 9 Because we have a fraction on the left side, we can cross multiply the denominator y by n - 9 [B]x =[/B] [B]y(n - 9)[/B]

x/y + 9 = n for y First, subtract 9 from each side to isolate the y term: x/y + 9 - 9 = n - 9 Cancel the 9's on the left side, and we get: x/y = n - 9 Cross multiply: x = y(n - 9) Divide each side by (n - 9): x/(n - 9) = y(n - 9)/(n - 9) Cancel the (n - 9) on the right side, and we get: y = [B]x/(n - 9)[/B]

x/y = z - 8 for x Cross multiply: [B]x = y(z - 8)[/B]

x/y = z - 8 for x Multiply each side by y to isolate x: y*(x/y) = y(z - 8) The y's cancel out on the left side, so we have: x = [B]y(z - 8)[/B]

x/y = z - 8 for x We start by seeing that x is isolated. To remove y from the left side, we multiply each side of the equation by y: xy/y = y(z - 8) Cancelling y on the left side, we get our answer of: x = [B]y(z - 8) [MEDIA=youtube]_HNyGlnnQdQ[/MEDIA][/B]

x=4, f(x)=x^4-64 Evaluate f(4): f(4) = 4^4 - 64 f(4) = 256 - 64 f(4) = [B]192[/B]

Xavier has $132 to buy a video game. Each game costs $12. Write an equation to find the number of games Xavier can purchase. Let g be the number of games, we have a cost function C(g) C(g) = 12g We want to find g such that C(g) = 132 12g = 132 Divide each side by 12 [B]g = 11[/B]

Y add z then divide by x y add z: y + z Then divide by x means we divide the sum (y + z) by x [B](y + z)/x[/B]

Multiply each side by 2 to isolate y. y +2c = 2d Subtract 2c from each side of the equation: y = 2d - 2c This can also be written y = 2(d - c)

Yosemite National Park charges $7 per person for an all day admission to the park. The total cost for n people to go to the park all day is given by the expression 7n. 8 friends go to the park on Saturday. What is the total cost of admission? We want to evaluate f(n) = 7n for n = 8 f(8) = 7(8) = [B]56[/B]

You and a friend collect acorns from a field. After g minutes u have collected(10 + 2g) acorns and your friend has collected (5g - 2) acorns. How many total acorns have you and your friend collected Add both acorn collections together: (10 + 2g) + (5g - 2) Group like terms: (5 + 2)g + 10 - 2 [B]7g + 8[/B]

You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $15 each and you paid $6.50 a piece plus a $50 set-up fee and $25 for shipping. How many shirts do you have to sell to break even? Round to the nearest whole number. [U]Step 1: Calculate Your Cost Function C(s) where s is the number of t-shirts[/U] C(s) = Cost per Shirt * (s) Shirts + Set-up Fee + Shipping C(s) = $6.50s + $50 + $25 C(s) = $6.50s + 75 [U]Step 2: Calculate Your Revenue Function R(s) where s is the number of t-shirts[/U] R(s) = Price Per Shirt * (s) Shirts R(s) = $15s [U]Step 3: Calculate Break-Even Point[/U] Break Even is where Cost = Revenue. Set C(s) = R(s) $6.50s + 75 = $15s [U]Step 4: Subtract 6.5s from each side[/U] 8.50s = 75 [U]Step 5: Solve for s[/U] [URL=' this through our equation calculator[/URL] to get s = 8.824. We round up to the next integer to get [B]s = 9[/B]. [B][URL=' Live Session[/URL][/B]

You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen? Let n be our original number. Square the number means we raise n to the power of 2: n^2 Multiply the result by 2: 2n^2 And then add three: 2n^2 + 3 If the friend's final answer is 53, this means we set 2n^2 + 3 equal to 53: 2n^2 + 3 = 53 To solve for n, we subtract 3 from each side, to isolate the n term: 2n^2 + 3 - 3 = 53 - 3 Cancel the 3's on the left side, and we get: 2n^2 = 50 Divide each side of the equation by 2: 2n^2/2 = 50/2 Cancel the 2's, we get: n^2 = 25 Take the square root of 25 n = +-sqrt(25) n = +-5 We are told the number is positive, so we discard the negative square root and get: n = [B]5[/B]

You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save 75 per week, and your friend saves 50 per week. When vacation time comes, you have 950, and your friend has 800. How much did you start with, and for how many weeks did you save? [U]Let w be the number of weeks. Set up two equations where s is the starting amount:[/U] (1) s + 75w =950 (2) s + 50w = 800 [U]Rearrange (1) into (3) to solve for s by subtracting 75w[/U] (3) s = 950 - 75w [U]Rearrange (2) into (4) to solve for s by subtracting 50w[/U] (4) s = 800 - 50w [U]Set (3) and (4) equal to each other so solve for w[/U] 950 - 75w = 800 - 50w [U]Add 75w to each side, and subtract 950 from each side:[/U] 25w = 150 [U]Divide each side by w[/U] [B]w = 6[/B] Now plug w = 6 into (3) s = 950 - 75(6) s = 950 - 450 [B]s = 500[/B]

You are baking muffins for your class. There are 17 total students in your class and you have baked 5 muffins. Write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. Write your equation so that the units on each side of the equation are muffins per student. 2 muffins per student = 17*2 = 34 muffins. We have an equation with a given 5 muffins, how much do we need (x) to get to 34 muffins (2 per student): x + 5 = 34 To solve for x, we type this equation into our search engine and we get: x = [B]29[/B]

You are buying boxes of cookies at a bakery. Each box of cookies costs $4. In the equation below, c represents the number of boxes of cookies you buy, and d represents the amount the cookies will cost you (in dollars). The relationship between these two variables can be expressed by the following equation: d=4c. Identify the dependent and independent variables. [B]The variable d is dependent, and c is independent since the value of d is determined by c.[/B]

You are comparing the costs of producing shoes at two different manufacturers. Company 1 charges $5 per pair of shoes plus a $650 flat fee. Company 2 charges $4 per pair of shoes plus a $700 flat fee. How many pairs of shoes are produced when the total costs for both companies are equal? Let s be the number of shoes. We have two equations: (1) C = 5s + 650 (2) C = 4s + 700 Set the costs equal to each other 5s + 650 = 4s + 700 Subtract 4s from each side s + 650 = 700 Subtract 650 from each side [B]s =50[/B]

You are heading to Cedar Point for the day. It costs $50 to get in to the park and each ride costs $2 for a ticket. Write an expression for the total cost of going to Cedar Point where r is the number of rides. Set up the cost equation C(r): C(r) = Cost per ride * r rides + Park Fee [B]C(r) = 2r + 50[/B]

You are making identical gift bags using 24 candles and 36 bottles of lotion. What is the greatest number of gift bags you can make with no items left over? We take the greatest common factor [URL=' (24, 36) = 12[/URL] So we have a ratio of 24/12 = 2 candles and 36/12 = 3 bottles of lotion per bag giving us [B]12 bags[/B].

You are parking your car in a garage. The first hour is free but every additional hour is 2 dollars. You parked for 3.25 hours. What is the cost? [U]Calculate the number of paid hours:[/U] Paid Hours = Total Hours - 1 (since first hour is free) Paid Hours = 3.25 - 1 Paid Hours = 2.25 [U]Calculate the total cost:[/U] Total Cost = Hourly Rate * Paid Hours Total Cost = 2 * 2.25 Paid Hours = [B]$4.50[/B]

You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet. Company A charges $2.99 per square foot plus a $200 installation charge. Company B charges $19.99 per square yard plus a $500 installation charge. What is the best deal? Did you notice the word snuck in on this problem? Company B is given in square [I][B]yards[/B][/I], not feet. Let's convert their price to square feet to match company A. [U]Company B conversion:[/U] Since we have 1 square yard = 3 feet * 3 feet = 9 square feet, we need to solve the following proportion: $19.99/square yard * 1 square yard/9 feet = $19.99 square yard / 9 feet = $2.22 / square foot. Now, let's set up the cost equations C(s) for each Company in square feet (s) [LIST] [*]Company A: C(s) = 200 + 2.99s [*]Company B: C(s) = 500 + 2.22s [/LIST] The problem asks for s = 30 feet * 50 feet = 1500 square feet. So we want to calculate C(1500) [U]Company A:[/U] C(1500) = 200 + 2.99(1500) C(1500) = 200 + 4485 C(1500) = 4685 [U]Company B:[/U] C(1500) = 500 + 2.22(1500) C(1500) = 500 + 3330 C(1500) = 3830 Since [B]Company B[/B] has the lower cost per square foot, they are the better buy.

You are using a spinner with the numbers 1-10 on it. Find the probability that the pointer will stop on an odd number or a number less than 4. We want P(odd number) or P(n<4). [LIST] [*]Odd numbers are {1, 3, 5, 7, 9} [*]n < 4 is {1, 2, 3} [/LIST] We want the union of these 2 sets: {1, 2, 3, 5, 7, 9} We have 6 possible pointers in a set of 10. [B]6/10 = 3/5 = 0.6 or 60%[/B]

You borrowed $25 from your friend. You paid him back in full after 6 months. He charged $2 for interest. What was the annual simple interest rate that he charged you? Use the formula: I = Prt. We have I = 2, P = 25, t = 0.5 2 = 25(r)0.5 Divide each side by 0.5 4 = 25r Divide each side by 25 r = 4/25 [B]r = 0.16[/B] As a percentage, this is [B]16%[/B]

You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase is $19.08, which includes 6% sales tax. Write and solve an equation to find the cost of the cat food. Our purchase includes at cat litter and cat food. Adding those together, we're given: 12.25 + x = 19.08 To solve for x, [URL=' type this equation into our search engine[/URL], and we get: x = 6.83 Since the cat food includes sales tax, we need to remove the sales tax of 6% to get the original purchase price. Original purchase price = After tax price / (1 + tax rate) Original purchase price = 6.83/1.06 Original purchase price = [B]$6.44[/B]

You buy a house for $130,000. It appreciates 6% per year. How much is it worth in 10 years The accumulated value in n years for the house is: A(n) = 130,000(1.06)^n We want A(10) A(10) = 130,000(1.06)^10 A(10) =130,000*1.79084769654 A(10) = [B]232,810.20[/B]

You can afford monthly deposits of $270 into an account that pays 3.0% compounded monthly. How long will it be until you have $11,100 to buy a boat. Round to the next higher month. [U]Set up our accumulation expression:[/U] 270(1.03)^n = 11100 1.03^n = 41.1111111 [U]Take the natural log of both sides[/U] n * Ln(1.03) = 41.1111111 n = 3.71627843/0.0295588 n = 125.72 so round up to [B]126[/B]

You can get 2 different moving companies to help you move. The first one charges $150 up front then $38 an hour. The second one charges $230 then $30 an hour, at what exact time will Both companies cost the same [U]Company 1: We set up the cost equation C(h) where h is the number of hours[/U] C(h) = Hourly Rate * h + up front charge C(h) = 38h + 150 [U]Company 2: We set up the cost equation C(h) where h is the number of hours[/U] C(h) = Hourly Rate * h + up front charge C(h) = 30h + 230 The question asks for h when both cost equations C(h) are equal. So we set both C(h) equations equal to other: 38h + 150 = 30h + 230 To solve for h, we [URL=' this equation into our search engine [/URL]and we get: h = [B]10[/B]

You choose an alpha level of .01 and then analyze your data. (a) What is the probability that you will make a Type I error given that the null hypothesis is true? (b) What is the probability that you will make a Type I error given that the null hypothesis is false. [B](a) 0.01. Instead, α is the probability of a Type I error given that the null hypothesis is true. If the null hypothesis is false, then it is impossible to make a Type I error.[/B] [B](b) Impossible Instead, α is the probability of a Type I error given that the null hypothesis is true. If the null hypothesis is false, then it is impossible to make a Type I error.[/B]

You collect a total of 75 in donations from three people. The three donations are in the ratio 4:4:7. How much is each of the smaller donations? 4 + 4 + 7 = 15 Each person's donation ratio is: [LIST=1] [*]Donation 1 is 4/15 of 75 [*]Donation 2 is 4/15 of 75 [*]Donation 3 is 7/15 of 75 [/LIST] 4/15(75) = 5 * 4 = 20 7/15(75) = 5 * 7 = 35 Each person's donation amount is: [LIST=1] [*][B]$20[/B] [*][B]$20[/B] [*][B]$35[/B] [/LIST] Check out work: 20 + 20 + 35 = 75!

You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must you leave the money in the account to earn $500 in interest? The simple interest formula for the accumulated balance is: Prt = I We are given P = 2,000, r = 0.04, and I = 500. 2000(0.04)t = 500 80t = 500 Divide each side by 80 t = [B]6.25 years [MEDIA=youtube]Myz0FZgwZpk[/MEDIA][/B]

You deposit $750 in an account that earns 5% interest compounded quarterly. Show and solve a function that represents the balance after 4 years. The Accumulated Value (A) of a Balance B, with an interest rate per compounding period (i) for n periods is: A = B(1 + i)^n [U]Givens[/U] [LIST] [*]4 years of quarters = 4 * 4 = 16 quarters. So this is t. [*]Interest per quarter = 5/4 = 1.25% [*]Initial Balance (B) = 750. [/LIST] Using our [URL=' balance interest calculator[/URL], we get the accumulated value A: [B]$914.92[/B]

you draw a card at random from a deck that contains 3 black cards and 7 red cards what is the probability of you drawing a black card Total cards = 3 black + 7 red Total cards = 10 P(Black) = Black cards / Total Cards P(Black) = [B]3/10 or 0.3[/B]

You earn $7 for every ? hour you cut the grass. How much money do you make for 3 hours? 3 hours / 1/3 hour = 9 (1/3 blocks) So we have: 7 * 9 = [B]63[/B]

You earned $141 last week babysitting and cleaning. You earned $5 per hour babysitting and $7 per hour cleaning. You worked 9 more hours babysitting than cleaning. How many hours did you work last week? Let b be the hours of babysitting and c be the hours of cleaning. We're given two equations: [LIST=1] [*]b = c + 9 [*]5b + 7c = 141 [/LIST] Substitute equation (1) into (2): 5(c + 9) + 7c = 141 Multiply through: 5c + 45 + 7c = 141 Combine like terms: 12c + 45 = 141 [URL=' this equation into our search engine[/URL], we get: c = 8 Now substitute this value of c back into Equation (1): b = 8 + 9 b = 17 The total hours worked (t) is: t = b + c t = 17 + 8 t = [B]25[/B]

You go to your favorite restaurant. The bill for the food is $74.26. The tax on the bill will be 9%. You are planning on giving a tip on that total amount (bill and tax together) of 20%. What is your final bill, all taxes and tips included? [U]Calculate the after tax amount:[/U] After tax amount = Bill * (1 + Tax Rate) Since 9% = 0.09, we have: After tax amount = 74.26 * (1 + 0.09) After tax amount = 74.26 * 1.09 After tax amount = 80.94 [U]Calculate the Tip amount:[/U] Tip amount = After tax amount * tip percent Since 20% = 0.2, we have: Tip amount = 80.94 * 0.20 Tip amount = 16.19 [U]Calculate the final bill:[/U] Final Bill = After Tax Amount + Tip Amount Final Bill = 80.94 + 16.19 Final Bill = [B]97.13[/B]

You have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account and saves $19 per week. How many weeks will it take for you and your friend to have the same balance? [U]Set up the savings account S(w) for you where w is the number of weeks[/U] S(w) = 140 + 10w [U]Set up the savings account S(w) for your friend where w is the number of weeks[/U] S(w) = 95 + 19w The problem asks for the number of weeks (w) when the balances are the same. So set both equations equal to each other: 140 + 10w = 95 + 19w To solve this equation for w, [URL=' type it in the search engine[/URL] and get: w = [B]5[/B]

You have $250,000 in an IRA (Individual Retirement Account) at the time you retire. You have the option of investing this money in two funds: Fund A pays 5.4% annually and Fund B pays 7.9% annually. How should you divide your money between fund Fund A and Fund B to produce an annual interest income of $14,750? You should invest $______in Fund A and $___________in Fund B. Equation is x(.079) + (250,000 - x).054 = 14,750 .025x + 13,500 = 14,750 .025x = 1,250 [B]x = 50,000 for Fund A[/B] So at 5.4%, we have 250,000 - 50,000 = [B]200,000[/B] for the other fund B.

You have 30 DONUTS. 1/6 of them are Boston Cream. 2/5 of them are Maple. 3/10 of them are Chocolate Dip and 1/3 are Sprinkled. IS THIS EVEN POSSIBLE?? How many donuts OVER or UNDER am I? (Show your work and use EQUIVALENTS.) We use 30 as our common denominator. Let's get [I]equivalent fraction[/I]s for each donut type with a denominator of 30: [LIST] [*][URL=' = 5/30 [*][URL=' [/URL]= 12/30 [*][URL=' = 9/30 [*][URL=' = 10/30 [/LIST] Add up our numerators of the common denominator of 30: 5 + 12 + 9 + 10 = 36 So our fraction is 36/30. This makes our scenario [B]impossible[/B]. Fractions of the donut should add up to 1. Which would mean our numerators need to sum to 1 or less. Since 36 > 30, this scenario is [B]impossible.[/B]

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject? Let m be the math problems and s be the science problems. We have two equations: (1) m + s = 42 (2) m = s + 10 Substitute (2) into (1) (s + 10) + s = 42 Combine like terms 2s + 10 = 42 Subtract 10 from each side 2s = 32 Divide each side by 2 [B]s = 16[/B] So that means m = 16 + 10 --> [B]m = 26 (m, s) = (26, 16)[/B]

You have read a 247 page book for a class and decide to read 18 pages a night. How many pages are left in the book if you have been reading for n nights? Set up the remaining pages read function R(n). We have: [B]R(n) = 247 - 18n[/B]

You have saved $50 over the last two weeks and decide to treat yourself by buying some new clothes. You go to the store and find two shirts and three pairs of jeans you like. The two shirts are buy-one-get-one half off, at $22.35 each. The three pairs of jeans are buy-two-get-one-free, at $23.70. Tax Rate for Harmonized Sales Tax is 13% a. What would be the total for the two shirts (dont forget to include taxes)? b. What would be the total for the three pairs of jeans (dont forget to include taxes)? c. Which would you buy and why? a. Half of 22.35 is 11.18 So two shirts cost: 22.35 + 11.18 = 33.53 Cost with Tax of 13% is: 33.53 * 1.13 = [B]37.89 [/B] b. Three pairs of jeans are calculated by cost of 1 pair times 2 jeans and you get the third one free: 23.70 * 2 = 47.40 Cost with Tax of 13% is: 47.40 * 1.13 = [B]53.56 [/B] c. Calculate unit cost, which is cost per item Unit cost of Shirts = 37.89 / 2 = [B]18.95[/B] Unit cost of Jeans = 53.56 / 3 = [B]17.85 Buy the jeans since they have a lower unit cost[/B]

You need to hire a catering company to serve meals to guests at a wedding reception. Company A charges $500 plus $20 per guest. Company B charges $800 plus $16 per guest. For how many guests are the total costs the same at both companies? Set up the Cost equations for both companies where g is the number of guests: [LIST] [*]C(a) = 20g + 500 [*]C(b) = 16g + 800 [/LIST] Set each equation equal to each other and use our [URL=' solver[/URL] to get: [B]g = 75[/B]

You open a hat stand in the mall with an initial start-up cost of $1500 plus 50 cents for every hat you stock your booth with. a) What is your cost function? Set up the cost function C(h) where h is the number of hats you stock: C(h) = Cost per hat * h hats + Start Up Cost [B]C(h) = 0.5h + 1500[/B]

You open up a savings account. Your initial deposit is $300. You plan to add in $50 per month to save up for college. Write an equation to represent the situation. Let m be the number of months. We have a Savings account function S(m): S(m) = Monthly deposit * number of months + Initial Deposit [B]S(m) = 50m + 300[/B]

You owe $25 to a friend. You have paid back $12 but asked for another $8. How much do you owe? You pay back 12, so your balance is: -25 + 12 = -13 or you owe 13 You ask for (Borrow) another $8 -13 - 8 = [B]-21 or you owe 21[/B]

You purchase a car for $23,000. The car depreciates at a rate of 15% per year. Determine the value of the car after 7 years. Round your answer to the nearest cent. Set up the Depreciation equation: D(t) = 23,000/(1.15)^t We want D(7) D(7) = 23,000/(1.15)^7 D(7) = 23,000/2.66002 D(7) = [B]8,646.55[/B]

You purchase a new car for $35,000. The value of the car depreciates at a rate of 8.5% per year. If the rate of decrease continues, what is the value of your car in 5 years? Set up the depreciation function D(t), where t is the time in years from purchase. We have: D(t) = 35,000(1 - 0.085)^t Simplified, a decrease of 8.5% means it retains 91.5% of it's value each year, so we have: D(t) = 35,000(0.915)^t The problem asks for D(5) D(5) = 35,000(0.915)^5 D(5) = 35,000(0.64136531607) D(5) = $[B]22,447.79[/B]

You put $5500 in a bond fund which has an annual yield of 4.8%. How much interest will be earned in 23 years? Build the accumulation of principal. We multiply 5,500 times 1.048 raised to the 23rd power. Future Value = 5,500 (1.048)^23 Future Value =5,500(2.93974392046) Future Value = 16,168.59 The question asks for interest earned, so we find this below: Interest Earned = Future Value - Principal Interest Earned = 16,168.59 - 5,500 Interest Earned = [B]10,668.59[/B]

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour? Set up a proportion of text messages to minutes. Remember, there are 60 minutes in an hour, so we have: 9/12 = t/60 where t is the number of text messages in 60 minutes (1 hour) [URL=' this into the search engine[/URL], we get [B]t = 45[/B].

You rent skates for $5 and pay $1 an hour for skating per person. Write an equation. Let the number of hours be h. Our cost function C(h) is: C(h) = Cost per hour * hourly rate + rental fee Plugging in our numbers, we get: [B]C(h) = h + 5[/B]

P(X = 4) AND P(X is odd) Which means P(X = 1) + P(X = 3) [LIST] [*]P(X = 1) = 1/6 [*]P(X = 3) = 1/6 [*]P(X = 1) + P(X = 3) = 1/6 + 1/6 = 2/6 = [B]1/3[/B] [/LIST]

You roll a red die and a green die. What is the size of the sample space of all possible outcomes of rolling these two dice, given that the red die shows an even number and the green die shows an odd number greater than 1? [LIST] [*]Red Die Sample Space {2, 4, 6} [*]Green Die Sample Space {3, 5} [*]Total Sample Space {(2, 3), (2, 5), (4, 3), (4, 5), (6, 3), (6, 5)} [*]The sie of this is 6 elements. [/LIST]

You split $1,500 between two savings accounts. Account A pays 5% annual interest and Account B pays 4% annual interest. After one year, you have earned a total of $69.50 in interest. How much money did you invest in each account. Explain. Let a be the amount you invest in Account A. So this means you invested 1500 - A in account B. We have the following equation: 05a + (1500 - a).04 = 69.50 Simplifying, we get: 0.05a + 1560 - 0.04a = 69.50 0.01a + 60 = 69.50 Using our [URL=' solver[/URL], we get: [B]a = 950[/B] So this means Account B is b = 1500 - 950 = [B]550[/B]

you start with 150$ in year bank account if you save $28 a year with equation would model your savings find equation. We create a savings function S(y) where y is the number of years since the start. S(y) = Savings per year * y + initial savings [B]S(y) = 28y + 150[/B]

You started this year with $491 saved and you continue to save an additional $11 per month. Write an algebraic expression to represent the total amount of money saved after m months. Set up a savings function for m months [B]S(m) = 491 + 11m[/B]

You went to the State Fair and spent $20. If cotton candy costs $2 and a soda pop costs $1. Which equation represents the relation between the number of cotton candy (c) and soda pops (s) you can buy? Our total cost for 20 at the state fair is: Cost of Cotton Candy + Cost of Soda = 20 We know that price = cost * quantity, so we have: 2c + 1s = 20 Since 1s is written as s, we have: [B]2c + s = 20[/B]

You work for a remote manufacturing plant and have been asked to provide some data about the cost of specific amounts of remote each remote, r, costs $3 to make, in addition to $2000 for labor. Write an expression to represent the total cost of manufacturing a remote. Then, use the expression to answer the following question. What is the cost of producing 2000 remote controls? We've got 2 questions here. Question 1: We want the cost function C(r) where r is the number of remotes: C(r) = Variable Cost per unit * r units + Fixed Cost (labor) [B]C(r) = 3r + 2000 [/B] Question 2: What is the cost of producing 2000 remote controls. In this case, r = 2000, so we want C(2000) C(2000) = 3(2000) + 2000 C(2000) = 6000 + 2000 C(2000) = [B]$8000[/B]

Your bill for dinner, including a 7.25% sales tax, was $49.95. You want to leave a 15% tip on the cost of the dinner before the sales tax. Find the amount of the tip to the nearest dollar. Find the pretax cost: 49.95/1.0725 = 46.57 Now, add 15% tip to the pretax bill: 46.57(1.15) = [B]$53.56[/B]

your classmate asserted that x^2 - 4x - 12 and 12 - 4x - x^2 has the same factors is your classmate correct Factor x^2 - 4x - 12 using binomials: (x + 2)(x - 6) Therefore, factors are x = -2, x = 6 Factor 12 - 4x - x^2 -(x - 6)(x + 2) Therefore, factors are x = -2, x = -6 Because they don't have two matching factors, your classmate is [B]incorrect.[/B]

Your clothes washer stopped working during the spin cycle and you need to get a person in to fix the washer. Company A costs $20 for the visit and $15 for every hour the person is there to fix the problem. Company B costs $40 for the visit and $5 for every hour the person is there to fix the problem. When would Company B be cheaper than Company A? Set up the cost functions: [LIST] [*]Company A: C(h) = 15h + 20 [*]Company B: C(h) = 5h + 40 [/LIST] Set them equal to each other: 15h + 20 = 5h + 40 Using our [URL=' solver[/URL], we get h = 2. With [B]h = 3[/B] and beyond, Company B becomes cheaper than Company A.

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pitched in to make a total of $12.50 to buy snacks. The fruit drinks are $1.50 and the chips are $1.00. Your friends want you to buy a total of 10 items. How many drinks and how many chips were you able to purchase? Let c be the number of chips. Let f be the number of fruit drinks. We're given two equations: [LIST=1] [*]c + f = 10 [*]c + 1.5f = 12.50 [/LIST] Rearrange equation 1 by subtracting f from both sides: [LIST=1] [*]c = 10 - f [*]c + 1.5f = 12.50 [/LIST] Substitute equation (1) into equation (2): 10 - f + 1.5f = 12.50 To solve for f, we [URL=' this equation into our search engine[/URL] and we get: [B]f = 5[/B] Now, substitute this f = 5 value back into modified equation (1) above: c = 10 - 5 [B]c = 5[/B]

Your salary after a 5% increase if your salary before the increase was s. If we start with s, and get a 5% increase, we will have s + 0.05s. Factor our s: [B]s(1.05) or 1.05s[/B]

your starting salary at a new company is 45000. Each year you receive a 2% raise. How long will it take you to make $80000? Let y be the number of years of compounding the 2% raise. Since 2% as a decimal is 0.02, we have the following equation for compounding the salary: 45000 * (1.02)^y = 80000 Divide each side by 45000: (1.02)^y = 1.77777777778 To solve this equation for y, we [URL=' it in our search engine[/URL] and we get: y = [B]29.05[/B] [B]Or just over 29 years[/B]

Youre setting sales goals for next month. You base your goals on previous average sales. The actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units. What is the average number of units you can expect to sell next month? Find the average sales for the last four years: Average Sales = Total Sales / 4 Average Sales = (24 + 30 + 23 + 27) / 4 Average Sales = 104 / 4 Average Sales = [B]26 units[/B]

z , subtract 5 then times by 3 Take this algebraic expression two parts: [LIST] [*]z subtract 5: z - 5 [*][I]Then times by 3[/I] means we multiply the expression z - 5 by 3 [/LIST] [B]3(z - 5)[/B]

z = (x + y)/mx; Solve for x Cross multiply: zmx = x + y Subtract x from each side zmx - x = y Factor out x x(zm - 1) = y Divide each side by zm - 1 x = y/(zm - 1) [MEDIA=youtube]ksxCS3YlCwY[/MEDIA]

Free Z Score Lookup Calculator - Given a Z-score probability statement from the list below, this will determine the probability using the normal distribution z-table. * P(z < a) * P(z <= a) * P(z > a) * P(z >= a) * P(a < z < b) Calculates z score probability

z/w=x+z/x+y for z This is a literal equation. Let's isolate z on one side. Subtract z/x from each side. z/w - z/x = x + y Factor our z on the left side: z(1/w - 1/x) = x + y Divide each side by (1/w - 1/x) z = x + y/(1/w - 1/x) To remove reciprocals in the denominator, we rewrite 1/w - 1/x with a common denominator xw (x - w)/xw Then multiply x + y by the reciprocal z = [B](x + y)xw/(x - w)[/B]

z=m-x+y, for x This is a literal equation. Let's add subtract (m + y) from each side: z - (m + y) = m - x + y - (m + y) The m + y terms cancel on the right side, so we have: z - m - y = -x Multiply each side by -1 to isolate x: -1(z - m - y) = -(-x) x = [B]m + y - z[/B]

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same as subtracting 5 from the number then multiplying by 4. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We're given two expressions in relation to this number (x): [U]She subtracts 6 then multiplies the result by 5[/U] [LIST] [*]Subtract 6: x - 6 [*]Multiply the result by 5: 5(x - 6) [/LIST] [U]She subtracts 5 from the number then multiplying by 4[/U] [LIST] [*]Subtract 6: x - 5 [*]Multiply the result by 5: 4(x - 5) [/LIST] Finally, the expression [I]is the same as[/I] means an equation, so we set the first expression equal to the second expression to make the following equation: 5(x - 6) = 4(x - 5) Now, let's solve the equation for x. To do this, we [URL=' this equation into our search engine [/URL]and we get: x = [B]10[/B]

Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it take for the population of about 600,000 to turn into zombies? Let d = every 2 days. We set up the exponential equation 2 * 2^d = 600,000 Divide each side by 2: 2^d = 300000 To solve this equation for d, we [URL=' it in our math engine[/URL] and we get d = 18.19 (2 day periods) 18.19 * days per period = 36.38 total days Most problems like this ask you to round to full days, so we round up to [B]37 days[/B].

zy-dm=ky/t for y Isolate terms with y to solve this literal equation. Subtract zy from each side: zy - dm - zy = ky/t - zy Cancel the zy terms on the left side, we get: -dm = ky/t - zy Factor out y: y(k/t - z) = -dm Divide each side by (k/t - z) y = -dm/(k/t - z) (k/t - z) can be rewritten as (k - tz)/t We multiply -dm by the reciprocal of this quotient to get our simplified literal equation: y = [B]-dmt/(k - tz)[/B]

|(x-7)/5|<=4 Set up two equations: [LIST=1] [*](x-7)/5 <= 4 [*](x-7)/5 > -4 [/LIST] Cross Multiply (1): x - 7 <= 20 Add 7 to each side: x <= 27 Cross Multiply (2): x - 7 > -20 Add 7 to each side: x > -13

? = 5, ? = 4 ; calculate P(0 < x < 8) This is the same as P(x < 8) - P(x < 0). P(x < 8) [URL=' our calculator[/URL] is 0.773373 P(x < 0) [URL=' our calculator[/URL] is 0.10565 So we have 0.773373 - 0.10565 = [B]0.667723[/B]

(-1 x 2 x 3)(i x i x i) = 6i^3 -6i^3 = -6 x i^2 x I We know that i = sqrt(-1) i^2 = sqrt(-1) x sqrt(-1) i^2 = -1 -6(-1)(i) [B]6i [MEDIA=youtube]Na1B327NckM[/MEDIA][/B]